# A wire coil of 1000 turns is placed in a uniform magnetic field so that the lines of magnetic induction

A wire coil of 1000 turns is placed in a uniform magnetic field so that the lines of magnetic induction are perpendicular to the plane of the turns. When the coil is removed from the field, a charge of 0.001 C flows through it. Determine the magnetic induction if the loop area is 0.001 m2. The impedance of the coil circuit is 2 ohms.

N = 1000.

Q = 0.01 Cl.

B = 0 T.

S = 0.001 m2.

∠α = 0 °.

R = 2 ohms.

V – ?

Since the coil has N turns, Faraday’s law of electromagnetic induction will have the form: EMF = – N * ΔF / t.

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

Let us express the change in magnetic induction ΔB by the formula: ΔB = B – B0 = – B0.

EMF = N * B0 * S * cosα / t.

I = EMF / R = N * B0 * S * cosα / t * R.

Let’s write down the definition for the current strength: I = Q / t.

Q / t = N * B0 * S * cosα / t * R.

B0 = Q * R / N * S * cosα.

B0 = 0.01 C * 2 Ohm / 1000 * 0.001 m2 * cos 0 ° = 0.02 T.

Answer: the magnetic induction of the field was B0 = 0.02 T.

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