The plane of a square wire loop with a side l = 0.1 is perpendicular to the lines of the magnetic field, the induction modulus of which is B = 0.5 T. Determine what charge will flow through the loop when it is rotated through an angle of a = 60 °, if the loop resistance is r = 0.5 kOhm.
l = 0.1 m.
B = 0.5 T.
R = 0.5 kΩ = 500 Ω.
∠α1 = 0 °.
∠α2 = 60 °.
Let us write down Faraday’s law of electromagnetic induction: EMF = – ΔF / t, where EMF is the electromotive force, ΔF is the change in the magnetic flux, t is the time of the change in the magnetic flux.
The “-” sign indicates the direction of the induction current.
ΔФ = Ф2 – Ф1.
The magnetic flux is determined by the formula: F1 = B * S * cosα1.
Ф2 = B * S * cosα2
The area of the square frame S is expressed by the formula: S = l ^ 2.
EMF = ΔФ / t = – (Ф2 – Ф1) / t = (B * l ^ 2 * cosα2 – B * l ^ 2 * cosα1) / t = B * l ^ 2 * (cosα2 – cosα1) / t.
Let’s write Ohm’s law: I = EMF / R = B * l ^ 2 * (cosα2 – cosα1) / R * t.
I = q / t.
q / t = B * l ^ 2 * (cosα2 – cosα1) / R * t.
q = B * l ^ 2 * (cosα2 – cosα1) / R.
q = 0.5 T * (0.1 m) ^ 2 * (cos0 ° – cosα60 °) / 500 Ohm = 5 * 10 ^ -6 Cl.
Answer: charge q = 5 * 10 ^ -6 C will flow through the loop.
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