Which expression represents Faraday's law for induced emf due to a changing magnetic flux?

Which expression represents Faraday's law for induced emf due to a changing magnetic flux?

• A. ε = dΦ/dt
• B. ε = - dΦ/dt
• C. ε = - N dΦ/dt
• D. ε = ΔΦ/Δt

Answer: (B)

When magnetic flux through a loop changes, an emf is induced and its direction is such that it opposes the change (Lenz’s law). The rate at which the flux changes drives the induced emf, and the sign reflects that opposition. For a single loop, the induced emf is the negative time derivative of the flux: ε = - dΦ/dt. The negative sign is what makes the induced current produce a magnetic field that fights the change in flux. If you have a coil with N turns, you multiply by N to get the total emf: ε = - N dΦ/dt. The other forms either omit the sign, use a rough finite difference rather than the instantaneous rate, or apply the coil case when the problem doesn’t specify multiple turns.

When magnetic flux through a loop changes, an emf is induced and its direction is such that it opposes the change (Lenz’s law). The rate at which the flux changes drives the induced emf, and the sign reflects that opposition. For a single loop, the induced emf is the negative time derivative of the flux: ε = - dΦ/dt. The negative sign is what makes the induced current produce a magnetic field that fights the change in flux. If you have a coil with N turns, you multiply by N to get the total emf: ε = - N dΦ/dt. The other forms either omit the sign, use a rough finite difference rather than the instantaneous rate, or apply the coil case when the problem doesn’t specify multiple turns.