Electromagnetic Induction and Faraday's Law
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Questions and Answers

What happens to the magnetic flux through the loop as the current in the loop increases?

The magnetic flux through the loop also increases.

What is the direction of the magnetic field inside the coil in Fig. 28.2a?

To the right.

What is the effect of the self-induced emf on the battery's current?

It causes a gradual increase in the battery's current to its final value.

What is the name of the phenomenon that occurs when the loop opposes its own changing current?

<p>Self-induction.</p> Signup and view all the answers

What is the purpose of Faraday's law in this context?

<p>To describe the effect of increasing or decreasing the current.</p> Signup and view all the answers

What is the induced emf in the loop called?

<p>A self-induced emf or back emf.</p> Signup and view all the answers

What is the mutual emf induced in coil 2 when the current I1 varies with time?

<p>∈M2 = M21dl1/dt</p> Signup and view all the answers

If a current I2 in coil 2 varies with time, what is the mutual emf induced in coil 1?

<p>∈M1 = M12dl2/dt</p> Signup and view all the answers

What is the relationship between the emf produced in either coil and the rate of change of current in the other coil?

<p>The emf produced in either coil is proportional to the rate of change of current in the other coil.</p> Signup and view all the answers

What is the unit of mutual inductance?

<p>The henry</p> Signup and view all the answers

What are the self-inductances of coils 1 and 2 in Example 2.0?

<p>L1 = 0.2 mH, L2 = 0.1 mH</p> Signup and view all the answers

What is the rate of change of current in coil 1 in Example 2.0?

<p>4 A/s</p> Signup and view all the answers

What is the mutual emf induced in coil 2 in Example 2.0?

<p>10 mV</p> Signup and view all the answers

What is the purpose of finding the mutual inductance of the combination in Example 2.0?

<p>To find the total induced emf of the combination</p> Signup and view all the answers

What is the formula for current in a coil in terms of time?

<p>I = 0.5 - 0.2t</p> Signup and view all the answers

What is the unit of self-inductance?

<p>Henries (H)</p> Signup and view all the answers

What causes a self-induced emf in a coil?

<p>A changing current</p> Signup and view all the answers

What is the relationship between the mutual inductance of two coils and their geometry?

<p>The mutual inductance depends on the geometry of both coils</p> Signup and view all the answers

What is the unit of mutual inductance?

<p>Henries (H)</p> Signup and view all the answers

What is the dot product B·dA proportional to?

<p>An infinitesimal amount of magnetic flux</p> Signup and view all the answers

What is the formula for mutual inductance of coil 2 in terms of coil 1?

<p>M21 = N2φ21/I1</p> Signup and view all the answers

What is the effect of a changing current in one coil on another coil in close proximity?

<p>It induces a changing flux, which in turn induces an emf</p> Signup and view all the answers

What is the direction of the induced electromotive force given by?

<p>Lenz's law</p> Signup and view all the answers

What is the total flux linkage through coil 2 due to coil 1?

<p>N2φ21</p> Signup and view all the answers

What is the purpose of creating a tightly wound coil of wire in increasing the generated emf?

<p>To exploit flux linkage</p> Signup and view all the answers

What is the relationship between the induced electromotive force and the rate of change of the magnetic flux?

<p>The induced electromotive force is equal to the rate of change of the magnetic flux</p> Signup and view all the answers

What is the unit of the magnetic field strength?

<p>Tesla (T)</p> Signup and view all the answers

What is the effect of Lenz's law on the direction of the induced current?

<p>The induced current will flow in the direction that will oppose the change which produced it</p> Signup and view all the answers

How does the number of turns in a coil affect the generated emf?

<p>The generated emf is proportional to the number of turns</p> Signup and view all the answers

What is the purpose of Faraday's law of induction?

<p>To describe the relationship between the induced electromotive force and the rate of change of the magnetic flux</p> Signup and view all the answers

What is the unit of self-inductance?

<p>HENRY (H)</p> Signup and view all the answers

What causes an induced emf in a coil?

<p>CHANGE IN CURRENT</p> Signup and view all the answers

What is the formula to calculate the induced emf in a coil?

<p>ε = -L(dI/dt)</p> Signup and view all the answers

What is the unit of mutual inductance?

<p>HENRY (H)</p> Signup and view all the answers

What happens to the mutually-induced and self-induced emfs in two coils when the current is the same in both coils?

<p>THEY ARE IN THE SAME DIRECTION</p> Signup and view all the answers

What is the formula to calculate the inductance of a coil?

<p>L = N × Φ / I</p> Signup and view all the answers

What is the effect of a common iron core on the primary and secondary coils of a transformer?

<p>THEY HAVE A COMMON VALUE OF MAGNETIC FLUX</p> Signup and view all the answers

What is the unit of magnetic flux?

<p>WEBER (Wb)</p> Signup and view all the answers

Study Notes

Magnetic Flux and Induction

  • The dot product B·dA corresponds to an infinitesimal amount of magnetic flux.
  • Magnetic flux through a wire loop is proportional to the number of magnetic field lines that pass through the loop.
  • When the flux through the surface changes, Faraday's law of induction states that the wire loop acquires an electromotive force (emf).
  • The induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit: 𝑑𝜙𝐵/𝑑𝑡 = - ↋.

Electromotive Force (EMF)

  • The direction of the electromotive force is given by Lenz's law, which states that an induced current will flow in the direction that will oppose the change which produced it.
  • To increase the generated emf, a common approach is to exploit flux linkage by creating a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them: 𝑑𝜙𝐵/𝑑𝑡 = -N ↋.

Self-Inductance

  • Self-inductance is the effect of a changing current in a loop on itself, causing a gradual increase in the current to its final value.
  • The induced emf (or back emf) in a coil opposes the battery's emf and its current: ↋L = -L dI/dt.
  • Self-inductance can be calculated using the formula: L = - ↋L / (dI/dt).

Mutual Inductance

  • Mutual inductance occurs when two coils are in close proximity, and a changing current in one coil causes a changing flux through the second coil.
  • The emf induced in one coil due to the changing current in the other coil is proportional to the rate of change of current: ↋M = -M dI/dt.
  • Mutual inductance can be calculated using the formula: M = N2 Φ21 / I1.
  • The unit of mutual inductance is the henry.

Examples and Exercises

  • Example: Find the induced emf and current in a circuit when the magnetic field between the poles of the electromagnet is uniform at any time, but its magnitude is increasing at a rate of 0.020 T/s.
  • Exercise: Find the magnitude of the induced emf in a coil when its current changes uniformly from zero to 1A in 50ms.
  • Exercise: Find the self-inductance of a coil when the magnitude of the average induced emf is 5V when its current changes from −30 to +120mA during a period of 30ms.
  • Exercise: Find the mutual inductance of a combination of two coils when the current in one coil changes at a rate of 4A/s, and an emf of 10mV is induced in the other coil.

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Description

Understand the concept of magnetic flux, electromotive force and Faraday's law of induction. Learn how the changing flux through a surface induces an electromotive force in a closed circuit.

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