# A wire ring with a radius of r = 10 cm is in an alternating magnetic field, the induction of which changes according

**A wire ring with a radius of r = 10 cm is in an alternating magnetic field, the induction of which changes according to the law B = Kt, where K = 2 * 10 ^ -4 T / s. The lines of magnetic induction are perpendicular to the plane of the ring. Ring resistance R = 0.6 ohm. What is the current in the ring.**

r = 10 cm = 0.1 m.

B (t) = K * t.

K = 2 * 10-4 T / s.

∠α = 0 °.

R = 0.6 ohm.

I -?

We express the current strength in the ring I according to Ohm’s law: I = EMF / R.

EMF of induction is expressed by Faraday’s law: EMF = ΔF / t.

Since the area of the ring does not change, the change in the magnetic flux is found by the formula: ΔФ = ΔB * S * cosα.

S = P * r2.

We express the change in magnetic induction ΔB by ΔB = B (t) = K * t.

I = ΔB * S * cosα / t * R = K * t * S * cos α / t * R = K * P * r2 * cosα / R =

I = 2 * 10-4 T / s * 3.14 * cos0 ° * (0.1 m) 2 / 0.6 Ohm = 0.1 * 10-4 A.

Answer: the current in the ring was I = 0.1 * 10-4 A.