Which expression correctly relates induced EMF to flux linkage in a coil?

Which expression correctly relates induced EMF to flux linkage in a coil?

• A. e = dλ/dt, λ = N Φ
• B. e = - dλ/dt, λ = N Φ
• C. e = - dΦ/dt, λ = Φ / N
• D. e = - d(NΦ)/dt, λ = Φ

Answer: (B)

The key idea is that the induced EMF in a coil is tied to how fast the total flux linked by the coil changes. That total flux linkage is the flux through one turn multiplied by the number of turns: λ = NΦ. Faraday’s law for a coil is then e = - dλ/dt, with the negative sign from Lenz’s law, meaning the induced EMF opposes the change in flux. So the correct relationship uses both pieces: e = - dλ/dt and λ = NΦ. If you combine them, you get e = - d(NΦ)/dt, which for a constant number of turns becomes e = - N dΦ/dt. The other forms omit the necessary sign or mix up the role of N and Φ, so they don’t correctly express how EMF relates to flux linkage in a coil.

The key idea is that the induced EMF in a coil is tied to how fast the total flux linked by the coil changes. That total flux linkage is the flux through one turn multiplied by the number of turns: λ = NΦ. Faraday’s law for a coil is then e = - dλ/dt, with the negative sign from Lenz’s law, meaning the induced EMF opposes the change in flux.

So the correct relationship uses both pieces: e = - dλ/dt and λ = NΦ. If you combine them, you get e = - d(NΦ)/dt, which for a constant number of turns becomes e = - N dΦ/dt. The other forms omit the necessary sign or mix up the role of N and Φ, so they don’t correctly express how EMF relates to flux linkage in a coil.