Which equation represents Faraday's law?

Which equation represents Faraday's law?

• A. ∇×E = -∂B/∂t
• B. ∇·E = ρ/ε0
• C. ∇×B = μ0 J + μ0 ε0 ∂E/∂t
• D. ∇·B = 0

Answer: (A)

Faraday's law describes how a changing magnetic field induces an electric field whose lines form closed loops around the region where the magnetic field changes. In differential form, this is written as ∇×E = -∂B/∂t. The curl of E being nonzero shows that the electric field is circulating rather than arising from static charges, and the negative sign embodies Lenz's law: the induced electric field acts to oppose the change in magnetic flux. This equation is the precise mathematical statement of electromagnetic induction. The other equations shown correspond to Gauss’s law for electricity (divergence of E relates to charge), the Ampère–Maxwell law (curl of B relates to current and the time rate of change of E), and Gauss’s law for magnetism (divergence of B is zero), which describe different aspects of electromagnetism.

Faraday's law describes how a changing magnetic field induces an electric field whose lines form closed loops around the region where the magnetic field changes. In differential form, this is written as ∇×E = -∂B/∂t. The curl of E being nonzero shows that the electric field is circulating rather than arising from static charges, and the negative sign embodies Lenz's law: the induced electric field acts to oppose the change in magnetic flux. This equation is the precise mathematical statement of electromagnetic induction. The other equations shown correspond to Gauss’s law for electricity (divergence of E relates to charge), the Ampère–Maxwell law (curl of B relates to current and the time rate of change of E), and Gauss’s law for magnetism (divergence of B is zero), which describe different aspects of electromagnetism.