Question

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.81 V and a current of 3.8 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What (a) emf and (b) current are induced in the square coil?

Answer 1

Area of the circular coil with radius R, Ac = R²
When the circular coil is re-formed to a square,
Circumference of the circular coil = Perimeter of the square.
2R = 4a
Where a is the side of the square.
a = R/2
Area of the square, As = a²
= ²R²/4
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Magnetic field induced in the circular coil, Ec = dB/dt * Ac
Where dB/dt is the change in the magnetic field.
0.81 = dB/dt * R² ...(1)

Magnetic field induced in the square loop, Es = dB/dt * As
Es = dB/dt * ​​​​​​​²R²/4 ...(2)
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a)
(2) /(1) gives
Es / 0.81 = /4
Es = 0.81 * /4
= 0.64 V
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b)
Resistance of the wire remain the same,
R = Ec/I
= 0.81 / 3.8
= 0.21 Ohm

Current in the square loop,
Is = Vs/R
= 0.64 / 0.21
= 3.0 A