A loop with a radius of 1 cm is in a magnetic field with a strength of 20 kA / m.

A loop with a radius of 1 cm is in a magnetic field with a strength of 20 kA / m. The plane of the loop is perpendicular to the field induction lines. What is the resistance of the loop if, when the field strength decreases to zero, a charge of 1 mC flows through it?

r = 1 cm = 0.01 m.

H0 = 20 kA / m = 20,000 A / m.

H = 0 A / m.

μ0 = 1.25 m * 10-6 m * kg / s2 * A2.

∠α = 90.

q = 1 mC = 0.001 Cl.

R -?

I = EMF / R – Ohm’s law for a closed loop ..

R = EMF / I.

EMF = ΔФ / t – Faraday’s law of electromagnetic induction.

ΔФ = ΔВ * S * cosα = μ0 * ΔH * P * r2 * cosα.

ΔH = H0 – H.

I = q / t – determination of the current strength.

R = μ0 * H * P * r ^ 2 * cosα * t / t * q = μ0 * H0 * P * r ^ 2 * cosα / q.

R = 1.25 m * 10 ^ -6 m * kg / s2 * A2 * 20,000 A / m * 3.14 * (0.01 m) ^ 2 * cos900 / 0.001 Cl = 0.00785 Ohm.

Answer: the coil has a resistance R = 0.00785 Ohm.