Which statement correctly describes the sign of the induced EMF according to Faraday's law?

Which statement correctly describes the sign of the induced EMF according to Faraday's law?

• A. The induced EMF is zero when flux linkage changes.
• B. The induced EMF is proportional to dλ/dt with a negative sign: e = - dλ/dt; the negative sign indicates opposition to the change in flux linkage.
• C. The induced EMF is proportional to dλ/dt with a positive sign.
• D. The induced EMF is independent of the rate of change of flux linkage.

Answer: (B)

Faraday's law gives the induced EMF as minus the rate of change of the magnetic flux linkage through the circuit. In symbols, e = - dλ/dt, where λ = NΦ. The negative sign expresses Lenz's law: the induced EMF acts to oppose the change in flux. So if the flux linkage is increasing, the induced EMF drives a current that tries to reduce that increase; if the flux linkage is decreasing, it drives a current that tries to oppose the decrease. The magnitude scales with how fast the flux linkage is changing. The other statements miss this opposition or the dependence on the rate of change, or incorrectly claim EMF is zero or independent of the change.

Faraday's law gives the induced EMF as minus the rate of change of the magnetic flux linkage through the circuit. In symbols, e = - dλ/dt, where λ = NΦ. The negative sign expresses Lenz's law: the induced EMF acts to oppose the change in flux. So if the flux linkage is increasing, the induced EMF drives a current that tries to reduce that increase; if the flux linkage is decreasing, it drives a current that tries to oppose the decrease. The magnitude scales with how fast the flux linkage is changing. The other statements miss this opposition or the dependence on the rate of change, or incorrectly claim EMF is zero or independent of the change.