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This square solenoid has sides length 25 cm, and 100 turns of wire. The resistance is 10 ohms. Find the magnitude of the induced emf in the coil if the magnetic field of 10 T is passing through the face of the loop as pictured. What is the induced current in the wire. Find the emf and current if the solenoid was a circle with radius 25 cm instead of a square.

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Manetho

Explanation:

Area of square = 25^2 = 625 cm^2 or  = 0.0625 m^2

number of turns = 100

Solenoid resistance = 10 ohms

now we know , Φ = B.A

where , Φ = magnetic flux, B= magnetic field strength, and A = area.

Φ = 10 × 0.0625 = 0.625 W

induced emf ε = dΦ/dt = d(BA)/dt  =0

This is because both B and A are constants.

⇒ Induced current is also zero.

Replacing square by a circle will not change situation as the value of B and A will remain constant with time hence, no emf induced, so no current induced.

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