A square frame with a side of 6.8 cm, made of copper wire with a cross-sectional area of 1 mm2

A square frame with a side of 6.8 cm, made of copper wire with a cross-sectional area of 1 mm2, is placed in a uniform magnetic field perpendicular to the lines of induction. The magnetic field induction changes uniformly by 0.002 T in 0.1 s. What is the current strength in the frame? The specific resistance of copper is 1.7 · 10-8 Ohm · m.

a = 6.8 cm = 0.068 m.

S = 1 mm2 = 1 * 10 ^ -6 m2.

ΔB = 0.002 T.

t = 0.1 s.

ρ = 1.7 * 10 ^ -8 Ohm * m.

I -?

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

EMF = ΔB * a ^ 2 / t is Faraday’s law of electromagnetic induction, where a ^ 2 is the area of a square frame.

The resistance of the frame R is expressed by the formula: R = ρ * L / S = ρ * 4 * a / S, where L is the length of the conductor, the perimeter of the square frame.

Let us express the value of the current strength: I = ΔB * a ^ 2 * S / ρ * 4 * a * t = ΔB * a * S / ρ * 4 * t.

I = 0.002 T * 0.068 m * 1 * 10 ^ -6 m2 / 1.7 * 10 ^ -8 Ohm * m * 4 * 0.1 s = 0.02 A.

Answer: the current in the square frame will be I = 0.02 A.