The square frame is placed in a uniform magnetic field so that the normal to the plane of the frame makes an angle a = 60 * with the direction of the magnetic field. Frame side I = 10cm. Determine the induction of the magnetic field, if it is known that the EMF of the induction arising in the frame when the field is “turned off” during the time t = 0.01 s is equal to (EMF) = 50 mV
∠α = 60 °.
l = 10 cm = 0.1 m.
EMF = 50 mV = 50 * 10-3 V.
S = 1 mm2 = 1 * 10-6 m2.
t = 0.01 s.
B = 0 T.
Let us write down Faraday’s law of electromagnetic induction: EMF = – ΔФ / t, where ΔФ is the change in magnetic flux, t is the time during which the magnetic flux has decreased.
Since the area of the frame does not change, then ΔФ = (В – В0) * S * cosα.
Since the frame has a square shape, its area S is expressed by the formula: S = l 2.
EMF = – (V – B0) * l 2 * cosα / t.
Since the magnetic field has decreased to B = 0 T, the formula will take the form: EMF = B0 * l 2 * cosα / t.
B0 = EMF * t / l 2 * cosα.
B0 = 50 * 10-3 V * 0.01 s / (0.1 m) 2 * cos60 ° = 0.057 T.
Answer: the magnetic induction of the field before switching off was B0 = 0.057 T.
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