Free Faraday's Law MCQs with Answers

1. Faraday's law states that the induced emf in a circuit is proportional to

• A. the magnetic flux through it
• B. the rate of change of magnetic flux linkage
• C. the current in it
• D. the resistance of the circuit

Explanation: It is the rate of change that matters, not the flux itself, so a coil sitting in a strong but steady field has no emf induced in it at all. Moving the magnet faster, using more turns or using a stronger field all increase the rate of change and therefore the emf. This is the single most important idea in the chapter.

2. A bar magnet is held stationary inside a coil. The induced emf in the coil is

• A. maximum
• B. zero
• C. half the maximum
• D. reversed in direction

Explanation: With the magnet at rest the flux linkage is constant, so its rate of change is zero and no emf is induced however strong the magnet. An emf appears only while the magnet is moving in or out, or while the field is changing. This is why a generator must keep rotating to keep producing electricity.

3. Self induction is the property by which a coil

• A. induces an emf in a neighbouring coil
• B. opposes any change in the current flowing through itself
• C. stores charge like a capacitor
• D. converts alternating current to direct current

Explanation: A changing current changes the coil's own flux, which by Lenz's law induces a back emf opposing that change, so an inductor resists sudden rises and falls of current. This is why a large spark appears when an inductive circuit is broken. Inducing an emf in a neighbouring coil is mutual induction instead.

4. The SI unit of inductance is the

• A. henry
• B. weber
• C. tesla
• D. farad

Explanation: One henry is the inductance of a coil in which a current changing at one ampere per second induces a back emf of one volt. The weber measures magnetic flux and the tesla flux density, while the farad belongs to capacitance. Getting these four units straight is worth a mark on its own in most papers.

5. In an alternating current generator, the emf induced in the rotating coil is maximum when the plane of the coil is

• A. perpendicular to the magnetic field
• B. parallel to the magnetic field
• C. at 45 degrees to the field
• D. irrelevant, since the emf is constant

Explanation: The emf depends on the rate of change of flux, not on the flux itself, and that rate is greatest when the coil is edge on to the field, precisely where the flux through it is momentarily zero. When the plane is perpendicular to the field the flux is maximum but is instantaneously stationary, so the emf is zero. This quarter cycle offset between flux and emf is what makes the output sinusoidal.

6. Which change would NOT increase the emf induced in a coil by a moving magnet?

• A. Moving the magnet faster
• B. Using a stronger magnet
• C. Increasing the number of turns on the coil
• D. Increasing the resistance of the coil

Explanation: The induced emf depends on flux, turns and speed of change, none of which is altered by the coil's resistance; resistance affects the induced current instead. The other three all raise the rate of change of flux linkage and so raise the emf. Distinguishing what changes the emf from what changes the current is exactly what this question tests.

7. A straight conductor of length 0.5 m moves at 4 m per second perpendicular to a field of 0.2 T. The emf induced across its ends is

• A. 0.4 V
• B. 0.1 V
• C. 4 V
• D. 2.5 V

Explanation: The motional emf is BvL, that is 0.2 multiplied by 4 multiplied by 0.5, giving 0.4 V. The formula assumes the conductor, the field and the motion are mutually perpendicular; otherwise only the perpendicular components count. This is the elementary form of Faraday's law, since the conductor sweeps out area at a rate vL.