experiment electromagnetic induction

20.3 Electromagnetic Induction

Section learning objectives.

By the end of this section, you will be able to do the following:

• Explain how a changing magnetic field produces a current in a wire
• Calculate induced electromotive force and current

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (G) investigate and describe the relationship between electric and magnetic fields in applications such as generators, motors, and transformers.

In addition, the OSX High School Physics Laboratory Manual addresses content in this section in the lab titled: Magnetism, as well as the following standards:

Section Key Terms

Changing Magnetic Fields

In the preceding section, we learned that a current creates a magnetic field. If nature is symmetrical, then perhaps a magnetic field can create a current. In 1831, some 12 years after the discovery that an electric current generates a magnetic field, English scientist Michael Faraday (1791–1862) and American scientist Joseph Henry (1797–1878) independently demonstrated that magnetic fields can produce currents. The basic process of generating currents with magnetic fields is called induction ; this process is also called magnetic induction to distinguish it from charging by induction, which uses the electrostatic Coulomb force.

When Faraday discovered what is now called Faraday’s law of induction, Queen Victoria asked him what possible use was electricity. “Madam,” he replied, “What good is a baby?” Today, currents induced by magnetic fields are essential to our technological society. The electric generator—found in everything from automobiles to bicycles to nuclear power plants—uses magnetism to generate electric current. Other devices that use magnetism to induce currents include pickup coils in electric guitars, transformers of every size, certain microphones, airport security gates, and damping mechanisms on sensitive chemical balances.

One experiment Faraday did to demonstrate magnetic induction was to move a bar magnet through a wire coil and measure the resulting electric current through the wire. A schematic of this experiment is shown in Figure 20.33 . He found that current is induced only when the magnet moves with respect to the coil. When the magnet is motionless with respect to the coil, no current is induced in the coil, as in Figure 20.33 . In addition, moving the magnet in the opposite direction (compare Figure 20.33 with Figure 20.33 ) or reversing the poles of the magnet (compare Figure 20.33 with Figure 20.33 ) results in a current in the opposite direction.

Virtual Physics

Faraday’s law.

Try this simulation to see how moving a magnet creates a current in a circuit. A light bulb lights up to show when current is flowing, and a voltmeter shows the voltage drop across the light bulb. Try moving the magnet through a four-turn coil and through a two-turn coil. For the same magnet speed, which coil produces a higher voltage?

• The sign of voltage will change because the direction of current flow will change by moving south pole of the magnet to the left.
• The sign of voltage will remain same because the direction of current flow will not change by moving south pole of the magnet to the left.
• The sign of voltage will change because the magnitude of current flow will change by moving south pole of the magnet to the left.
• The sign of voltage will remain same because the magnitude of current flow will not change by moving south pole of the magnet to the left.

Induced Electromotive Force

If a current is induced in the coil, Faraday reasoned that there must be what he called an electromotive force pushing the charges through the coil. This interpretation turned out to be incorrect; instead, the external source doing the work of moving the magnet adds energy to the charges in the coil. The energy added per unit charge has units of volts, so the electromotive force is actually a potential. Unfortunately, the name electromotive force stuck and with it the potential for confusing it with a real force. For this reason, we avoid the term electromotive force and just use the abbreviation emf , which has the mathematical symbol ε . ε . The emf may be defined as the rate at which energy is drawn from a source per unit current flowing through a circuit. Thus, emf is the energy per unit charge added by a source, which contrasts with voltage, which is the energy per unit charge released as the charges flow through a circuit.

To understand why an emf is generated in a coil due to a moving magnet, consider Figure 20.34 , which shows a bar magnet moving downward with respect to a wire loop. Initially, seven magnetic field lines are going through the loop (see left-hand image). Because the magnet is moving away from the coil, only five magnetic field lines are going through the loop after a short time Δ t Δ t (see right-hand image). Thus, when a change occurs in the number of magnetic field lines going through the area defined by the wire loop, an emf is induced in the wire loop. Experiments such as this show that the induced emf is proportional to the rate of change of the magnetic field. Mathematically, we express this as

where Δ B Δ B is the change in the magnitude in the magnetic field during time Δ t Δ t and A is the area of the loop.

Note that magnetic field lines that lie in the plane of the wire loop do not actually pass through the loop, as shown by the left-most loop in Figure 20.35 . In this figure, the arrow coming out of the loop is a vector whose magnitude is the area of the loop and whose direction is perpendicular to the plane of the loop. In Figure 20.35 , as the loop is rotated from θ = 90° θ = 90° to θ = 0° , θ = 0° , the contribution of the magnetic field lines to the emf increases. Thus, what is important in generating an emf in the wire loop is the component of the magnetic field that is perpendicular to the plane of the loop, which is B cos θ . B cos θ .

This is analogous to a sail in the wind. Think of the conducting loop as the sail and the magnetic field as the wind. To maximize the force of the wind on the sail, the sail is oriented so that its surface vector points in the same direction as the winds, as in the right-most loop in Figure 20.35 . When the sail is aligned so that its surface vector is perpendicular to the wind, as in the left-most loop in Figure 20.35 , then the wind exerts no force on the sail.

Thus, taking into account the angle of the magnetic field with respect to the area, the proportionality E ∝ Δ B / Δ t E ∝ Δ B / Δ t becomes

Another way to reduce the number of magnetic field lines that go through the conducting loop in Figure 20.35 is not to move the magnet but to make the loop smaller. Experiments show that changing the area of a conducting loop in a stable magnetic field induces an emf in the loop. Thus, the emf produced in a conducting loop is proportional to the rate of change of the product of the perpendicular magnetic field and the loop area

where B cos θ B cos θ is the perpendicular magnetic field and A is the area of the loop. The product B A cos θ B A cos θ is very important. It is proportional to the number of magnetic field lines that pass perpendicularly through a surface of area A . Going back to our sail analogy, it would be proportional to the force of the wind on the sail. It is called the magnetic flux and is represented by Φ Φ .

The unit of magnetic flux is the weber (Wb), which is magnetic field per unit area, or T/m 2 . The weber is also a volt second (Vs).

The induced emf is in fact proportional to the rate of change of the magnetic flux through a conducting loop.

Finally, for a coil made from N loops, the emf is N times stronger than for a single loop. Thus, the emf induced by a changing magnetic field in a coil of N loops is

The last question to answer before we can change the proportionality into an equation is “In what direction does the current flow?” The Russian scientist Heinrich Lenz (1804–1865) explained that the current flows in the direction that creates a magnetic field that tries to keep the flux constant in the loop. For example, consider again Figure 20.34 . The motion of the bar magnet causes the number of upward-pointing magnetic field lines that go through the loop to decrease. Therefore, an emf is generated in the loop that drives a current in the direction that creates more upward-pointing magnetic field lines. By using the right-hand rule, we see that this current must flow in the direction shown in the figure. To express the fact that the induced emf acts to counter the change in the magnetic flux through a wire loop, a minus sign is introduced into the proportionality ε ∝ Δ Φ / Δ t . ε ∝ Δ Φ / Δ t . , which gives Faraday’s law of induction.

Lenz’s law is very important. To better understand it, consider Figure 20.36 , which shows a magnet moving with respect to a wire coil and the direction of the resulting current in the coil. In the top row, the north pole of the magnet approaches the coil, so the magnetic field lines from the magnet point toward the coil. Thus, the magnetic field B → mag = B mag ( x ^ ) B → mag = B mag ( x ^ ) pointing to the right increases in the coil. According to Lenz’s law, the emf produced in the coil will drive a current in the direction that creates a magnetic field B → coil = B coil ( − x ^ ) B → coil = B coil ( − x ^ ) inside the coil pointing to the left. This will counter the increase in magnetic flux pointing to the right. To see which way the current must flow, point your right thumb in the desired direction of the magnetic field B → coil, B → coil, and the current will flow in the direction indicated by curling your right fingers. This is shown by the image of the right hand in the top row of Figure 20.36 . Thus, the current must flow in the direction shown in Figure 4(a) .

In Figure 4(b) , the direction in which the magnet moves is reversed. In the coil, the right-pointing magnetic field B → mag B → mag due to the moving magnet decreases. Lenz’s law says that, to counter this decrease, the emf will drive a current that creates an additional right-pointing magnetic field B → coil B → coil in the coil. Again, point your right thumb in the desired direction of the magnetic field, and the current will flow in the direction indicate by curling your right fingers ( Figure 4(b) ).

Finally, in Figure 4(c) , the magnet is reversed so that the south pole is nearest the coil. Now the magnetic field B → mag B → mag points toward the magnet instead of toward the coil. As the magnet approaches the coil, it causes the left-pointing magnetic field in the coil to increase. Lenz’s law tells us that the emf induced in the coil will drive a current in the direction that creates a magnetic field pointing to the right. This will counter the increasing magnetic flux pointing to the left due to the magnet. Using the right-hand rule again, as indicated in the figure, shows that the current must flow in the direction shown in Figure 4(c) .

Faraday’s Electromagnetic Lab

This simulation proposes several activities. For now, click on the tab Pickup Coil, which presents a bar magnet that you can move through a coil. As you do so, you can see the electrons move in the coil and a light bulb will light up or a voltmeter will indicate the voltage across a resistor. Note that the voltmeter allows you to see the sign of the voltage as you move the magnet about. You can also leave the bar magnet at rest and move the coil, although it is more difficult to observe the results.

• Yes, the current in the simulation flows as shown because the direction of current is opposite to the direction of flow of electrons.
• No, current in the simulation flows in the opposite direction because the direction of current is same to the direction of flow of electrons.

Watch Physics

Induced current in a wire.

This video explains how a current can be induced in a straight wire by moving it through a magnetic field. The lecturer uses the cross product , which a type of vector multiplication. Don’t worry if you are not familiar with this, it basically combines the right-hand rule for determining the force on the charges in the wire with the equation F = q v B sin θ . F = q v B sin θ .

Grasp Check

What emf is produced across a straight wire 0.50 m long moving at a velocity of (1.5 m/s) x ^ x ^ through a uniform magnetic field (0.30 T) ẑ ? The wire lies in the ŷ -direction. Also, which end of the wire is at the higher potential—let the lower end of the wire be at y = 0 and the upper end at y = 0.5 m)?

• 0.15 V and the lower end of the wire will be at higher potential
• 0.15 V and the upper end of the wire will be at higher potential
• 0.075 V and the lower end of the wire will be at higher potential
• 0.075 V and the upper end of the wire will be at higher potential

Worked Example

Emf induced in conducing coil by moving magnet.

Imagine a magnetic field goes through a coil in the direction indicated in Figure 20.37 . The coil diameter is 2.0 cm. If the magnetic field goes from 0.020 to 0.010 T in 34 s, what is the direction and magnitude of the induced current? Assume the coil has a resistance of 0.1 Ω. Ω.

Use the equation ε = − N Δ Φ / Δ t ε = − N Δ Φ / Δ t to find the induced emf in the coil, where Δ t = 34 s Δ t = 34 s . Counting the number of loops in the solenoid, we find it has 16 loops, so N = 16 . N = 16 . Use the equation Φ = B A cos θ Φ = B A cos θ to calculate the magnetic flux

where d is the diameter of the solenoid and we have used cos 0° = 1 . cos 0° = 1 . Because the area of the solenoid does not vary, the change in the magnetic of the flux through the solenoid is

Once we find the emf, we can use Ohm’s law, ε = I R , ε = I R , to find the current.

Finally, Lenz’s law tells us that the current should produce a magnetic field that acts to oppose the decrease in the applied magnetic field. Thus, the current should produce a magnetic field to the right.

Combining equations ε = − N Δ Φ / Δ t ε = − N Δ Φ / Δ t and Φ = B A cos θ Φ = B A cos θ gives

Solving Ohm’s law for the current and using this result gives

Lenz’s law tells us that the current must produce a magnetic field to the right. Thus, we point our right thumb to the right and curl our right fingers around the solenoid. The current must flow in the direction in which our fingers are pointing, so it enters at the left end of the solenoid and exits at the right end.

Let’s see if the minus sign makes sense in Faraday’s law of induction. Define the direction of the magnetic field to be the positive direction. This means the change in the magnetic field is negative, as we found above. The minus sign in Faraday’s law of induction negates the negative change in the magnetic field, leaving us with a positive current. Therefore, the current must flow in the direction of the magnetic field, which is what we found.

Now try defining the positive direction to be the direction opposite that of the magnetic field, that is positive is to the left in Figure 20.37 . In this case, you will find a negative current. But since the positive direction is to the left, a negative current must flow to the right, which again agrees with what we found by using Lenz’s law.

Magnetic Induction due to Changing Circuit Size

The circuit shown in Figure 20.38 consists of a U-shaped wire with a resistor and with the ends connected by a sliding conducting rod. The magnetic field filling the area enclosed by the circuit is constant at 0.01 T. If the rod is pulled to the right at speed v = 0.50 m/s, v = 0.50 m/s, what current is induced in the circuit and in what direction does the current flow?

We again use Faraday’s law of induction, E = − N Δ Φ Δ t , E = − N Δ Φ Δ t , although this time the magnetic field is constant and the area enclosed by the circuit changes. The circuit contains a single loop, so N = 1 . N = 1 . The rate of change of the area is Δ A Δ t = v ℓ . Δ A Δ t = v ℓ . Thus the rate of change of the magnetic flux is

where we have used the fact that the angle θ θ between the area vector and the magnetic field is 0°. Once we know the emf, we can find the current by using Ohm’s law. To find the direction of the current, we apply Lenz’s law.

Faraday’s law of induction gives

Solving Ohm’s law for the current and using the previous result for emf gives

As the rod slides to the right, the magnetic flux passing through the circuit increases. Lenz’s law tells us that the current induced will create a magnetic field that will counter this increase. Thus, the magnetic field created by the induced current must be into the page. Curling your right-hand fingers around the loop in the clockwise direction makes your right thumb point into the page, which is the desired direction of the magnetic field. Thus, the current must flow in the clockwise direction around the circuit.

Is energy conserved in this circuit? An external agent must pull on the rod with sufficient force to just balance the force on a current-carrying wire in a magnetic field—recall that F = I ℓ B sin θ . F = I ℓ B sin θ . The rate at which this force does work on the rod should be balanced by the rate at which the circuit dissipates power. Using F = I ℓ B sin θ , F = I ℓ B sin θ , the force required to pull the wire at a constant speed v is

where we used the fact that the angle θ θ between the current and the magnetic field is 90° . 90° . Inserting our expression above for the current into this equation gives

The power contributed by the agent pulling the rod is F pull v , or F pull v , or

The power dissipated by the circuit is

We thus see that P pull + P dissipated = 0 , P pull + P dissipated = 0 , which means that power is conserved in the system consisting of the circuit and the agent that pulls the rod. Thus, energy is conserved in this system.

Practice Problems

The magnetic flux through a single wire loop changes from 3.5 Wb to 1.5 Wb in 2.0 s. What emf is induced in the loop?

What is the emf for a 10-turn coil through which the flux changes at 10 Wb/s?

Check Your Understanding

• An electric current is induced if a bar magnet is placed near the wire loop.
• An electric current is induced if a wire loop is wound around the bar magnet.
• An electric current is induced if a bar magnet is moved through the wire loop.
• An electric current is induced if a bar magnet is placed in contact with the wire loop.
• Induced current can be created by changing the size of the wire loop only.
• Induced current can be created by changing the orientation of the wire loop only.
• Induced current can be created by changing the strength of the magnetic field only.
• Induced current can be created by changing the strength of the magnetic field, changing the size of the wire loop, or changing the orientation of the wire loop.

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AP®︎/College Physics 2

Course: ap®︎/college physics 2   >   unit 4, electromagnetic induction.

• Magnetic flux and Faraday's law
• Faraday's Law
• Faraday's law - magnitude of induced emf (average)
• Lenz's law
• Lenz's law - iii
• Emf induced in rod traveling through magnetic field

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Video transcript

The National MagLab is funded by the National Science Foundation and the State of Florida.

Electromagnetic Induction

When a permanent magnet is moved inside of a copper wire coil, electrical current flows inside of the wire. This important physics phenomenon is called electromagnetic induction.

In 1831, the great experimentalist Michael Faraday set out to prove electricity could be generated from magnetism. He created numerous experiments, including the simple but illustrious setup of the copper wire and permanent magnet . Faraday wrapped the copper wire around a paper cylinder and attached the ends of the coil to a galvanometer, which is a device that detects and measures electrical current.

Instructions

• Click and drag the bar magnet back and forth inside the coil.
• Observe the galvanometer and see that there is only current detected when the magnet is in motion.
• Increase the speed of the magnet’s movement (by dragging the magnet faster) to see how this increases the current.
• Add turns to the wire and notice how the reading on the galvanometer increases.
• Flip the magnet. Watch how the direction of the field impacts the direction of the current (depicted with black arrows.)

When the permanent magnet moves inside of the coil, the mechanical energy of the movement is converted into electricity. While this experiment was uncomplicated, it was also revolutionary. Faraday’s work was translated into an equation by James Clerk Maxwell, who went on the expand on Faraday’s findings and create other equations that are the backbone of the study of electromagnetism. Electromagnetic induction is still crucial to the modern world, and is used in devices like generators, transformers, and electric motors. It can also be used to wirelessly charge devices like an electric toothbrush or phone.

To give credit where credit is due, Joseph Henry was not far behind in his independent discovery of electromagnetic induction in 1832. Dig deeper into the history of important scientists in our Pioneers section.

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Basic Projects and Test Equipment

• Intro Lab - How to Use a Voltmeter to Measure Voltage
• Intro Lab - How to Use an Ohmmeter to Measure Resistance
• Intro Lab - How to Use an Ammeter to Measure Current
• Intro Lab - Ohm’s Law
• Intro Lab - Resistor Power Dissipation
• Intro Lab - A Simple Lighting Circuit
• Intro Lab - Nonlinear Resistance
• Intro Lab - Circuit With a Switch
• Intro Lab - Build an Electromagnet

In this hands-on electronics experiment, you will learn about electromagnetic induction using an electromagnet and a permanent magnet.

Project overview.

Electromagnetic induction is a complementary phenomenon to electromagnetism . Instead of producing a magnetic field from electricity, we produce electricity from a magnetic field. There is one important difference, though, whereas electromagnetism produces a steady magnetic field from a steady electric current, electromagnetic induction requires motion between the magnet and the coil to produce a voltage . In this project, you measure electromagnetic induction using the test setup illustrated in Figure 1.

Figure 1. Circuit for measuring the induced voltage from the electromagnet.

Parts and materials.

• Electromagnet from the previous project:  building an electromagnet
• Permanent magnet

Learning Objectives

• Relationship between magnetic field strength and induced voltage

Instructions

Step 1:  Connect the multimeter to the coil, as illustrated in Figures 1 and 2, and set it to the most sensitive DC voltage range available. 

Figure 2.  The schematic diagram for measuring the induced voltage from the electromagnet.

If you are using an analog multimeter , be sure to use long jumper wires and locate the meter far away from the coil, as the magnetic field from the permanent magnet may affect the meter’s operation and produce false readings. Digital meters are unaffected by magnetic fields.

Step 2:  Measure the voltage output from the electromagnet. Hint: it should be zero! 

Step 3:  Move the magnet slowly to and from one end of the electromagnet, noting the polarity and magnitude of the induced voltage.

Step 4:  Experiment with moving the magnet, and discover for yourself what factor(s) determine the amount of voltage induced. Consider the distance from the electromagnet and speed of movement.

Step 5:  Repeat the process at the other end of the electromagnet coil and compare results.

Step 6: Repeat the process using the other end of the permanent magnet and compare.

Related Content

Learn more about the fundamentals behind this project in the resources below.

• Magnetism and Electromagnetism
• Electromagnetism

Worksheets:

• Basic Electromagnetism and Electromagnetic Induction Worksheet
• Intermediate Electromagnetism and Electromagnetic Induction Worksheet
• Advanced Electromagnetism and Electromagnetic Induction Worksheet
• Textbook Index
• Back To Index

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Science project, electromagnetic induction experiment.

Electricity is carried by current , or the flow of electrons. One useful characteristic of current is that it creates its own magnetic field. This is useful in many types of motors and appliances. Conduct this simple electromagnetic induction experiment to witness this phenomenon for yourself!

Observe how current can create a magnetic field.

What will happen when the battery is connected and the switch is turned on? Will the battery voltage make a difference in the magnetic field?

• Thin copper wire
• Long metal nail
• 12-V lantern battery
• 9-V battery
• Wire cutters
• Toggle switch
• Electrical tape
• Paper clips
• Cut a long length of wire and attached one end to the positive output of the toggle switch.
• Twist the wire at least 50 times around the nail to create a solenoid.
• Once the wire has covered the nail, tape the wire to the negative terminal of the 12V battery.
• Cut a short piece of wire to connect the positive terminal of the battery to the negative terminal of the toggle switch.

• Turn on the switch.
• Bring paper clips close to the nail. What happens? How many paper clips can you pick up?
• Repeat the experiment with the 9V battery.
• Repeat the experiment with the 9V and 12V batteries arranged in series (if you don’t know how to arrange batteries in series, check out this project that explains how).

The current running through the circuit will cause the nail to be magnetic and attract paper clips. The 12V battery will create a stronger magnet than the 9V battery. The series circuit will create a stronger magnet than the individual batteries did.

Electric currents always produce their own magnetic fields. This phenomenon is represented by the right-hand-rule:

If you make the “Thumbs-Up” sign with your hand like this:

The current will flow in the direction the thumb is pointing, and the magnetic field direction will be described by the direction of the fingers. This means when you change the direction of the current, you also change the direction of the magnetic field. Current flows (which means electrons flow) from the negative end of a battery through the wire to the positive end of the battery, which can help you determine what the direction of the magnetic field will be.

When the toggle switch is turned on, the current will flow from the negative terminal of the battery around the circuit to the positive terminal. When the current passes through the nail it induces , or creates, a magnetic field.  The 12V battery produces a larger voltage ; therefore, produces a higher current for a circuit of the same resistance. Larger currents will induce larger (and stronger!) magnetic fields, so the nail will attract more paperclips when using a larger voltage.

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Detection of stress distribution in surrounding rock of coal seam roadway based on charge induction principle, 1. introduction, 2. stress distribution in coal body mining, 3. mechanism of charge generation in stress-activated coals, 4. theoretical analysis of the relationship between charge induction intensity and stress level, 5. charge induction law test for graded loading coal bodies, 5.1. specimen preparation, 5.2. experiment system, 5.3. experiment methods and steps, 5.4. test results and analyses, 6. stress distribution charge detection test of roadway surrounding rock, 6.1. charge-monitoring equipment, 6.2. monitoring site and monitoring point layout, 6.3. monitoring results and analysis, 7. discussion and conclusions.

• The coal sample has charge and acoustic emission during the step loading process, and the magnitude of the induced charge and acoustic emission energy is in good agreement with the stress level. The charge induction signal is more sensitive to the high stress of constant load, which can indirectly reflect the stress level of the coal body.
• The induced charge is small when the drilling depth of the solid coal side seam is 1~4 m. When the drilling depth is 5~9 m, the induced charge increases significantly. When the drilling depth is more than 9 m, the induced charge is smaller and then is stable. With the increase in drilling depth, the inductive signal of charge on the solid coal side has a wave peak, the position of the wave peak is 8~9 m from the roadway, and the stress concentration coefficient is 1.3~1.4.
• The induced charge is small when the drilling depth of the coal seam on the side of the coal pillar is 1~4 m. When the drilling depth is 5~7 m, the induced charge increases significantly. When the drilling depth is more than 7 m, the induced charge is smaller and then increases steadily. With the increase in drilling depth, the charge induction signal on the side of the coal pillar has a secondary wave peak, and the position of the first wave peak is 7 m from the roadway with a stress concentration factor of 1.6.
• With the increase in drilling depth, the amount of induced charge and drill cuttings per meter is in good agreement with the stress distribution in the roadway perimeter rock, and the location of the peak charge and drill cuttings is in agreement with the reflected stress concentration factor. Compared with the drilling chip method, charge induction technology has the advantages of being portable and non-contact, with high inspection efficiency and no disruption to production.
• By analyzing the size and position of charges at various borehole depths, the depth of the plastic zone and the peak area of lateral abutment pressure can be determined. This analysis provides targeted guidance for preventing and controlling coal and rock dynamic disasters, such as rock burst.

Author Contributions

Data availability statement, conflicts of interest.

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Wang, G.; Du, L.; Fan, D.; Wang, A.; Shi, T.; Dai, L. Detection of Stress Distribution in Surrounding Rock of Coal Seam Roadway Based on Charge Induction Principle. Electronics 2024 , 13 , 3075. https://doi.org/10.3390/electronics13153075

Wang G, Du L, Fan D, Wang A, Shi T, Dai L. Detection of Stress Distribution in Surrounding Rock of Coal Seam Roadway Based on Charge Induction Principle. Electronics . 2024; 13(15):3075. https://doi.org/10.3390/electronics13153075

Wang, Gang, Lulu Du, Dewei Fan, Aiwen Wang, Tianwei Shi, and Lianpeng Dai. 2024. "Detection of Stress Distribution in Surrounding Rock of Coal Seam Roadway Based on Charge Induction Principle" Electronics 13, no. 15: 3075. https://doi.org/10.3390/electronics13153075

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• DOI: 10.1007/s11663-024-03211-1
• Corpus ID: 271626443

Numerical Simulation of Multi-physics Characteristics in Tundish with Channel Induction Heating

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