Ampere's Law relates the line integral of the magnetic field around a closed loop to what quantity?

• A. The line integral around a closed loop equals μ0 times the current enclosed
• B. The curl of E equals zero in steady state
• C. The energy stored in a magnetic field equals LI^2
• D. The speed of light equals frequency times wavelength

Answer: (A)

Magnetic fields created by currents circulate around the wires, and Ampere's law links how much circulation you get around a closed path to the amount of current passing through the loop’s interior. Specifically, for steady currents, the line integral of the magnetic field B around a closed loop equals μ0 times the current that threads the surface bounded by that loop. Here μ0 is the permeability of free space, a constant that sets the strength of the magnetic response.

So the quantity the line integral measures is the current enclosed by the loop, scaled by μ0: ∮ B · dl = μ0 I_enc.

For context, the other statements don’t describe this relationship: curl E = 0 describes the electric field in electrostatics, not the magnetic circulation around a loop; the energy expression and the wave relation involve different physics or conventions, not the line integral of B around a loop.