A rectangular circuit sits in a uniform magnetic field. It has a height of h = 0

Question

A rectangular circuit sits in a uniform magnetic field. It has a height of h = 0.8 m and width of w = 1.2 m and a resistor with R = 3 Ohm. The magnetic field points into the page and starts at a magnitude of B = 0.1 T and increases at a rate of 0.6 T/s. What is the magnetic flux, Phi_B, at the beginning when B = 0.1 T? What is the voltage induced in the loop? What current flows through the loop due to the induced voltage? Does the current flow CLOCKWISE or COUNTERCLOCKWISE? When the external magnetic field is at B = 2 T, what is the force on the left side (of length h = 0.8 m) due to the current flowing in the external magnetic field?

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW

where A = area = h * W

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of amgnetic flux

Part A:

magnetic flux phi = BA

phi = 0.1 * 1.2 * 0.8

phi = 0.096 Wb

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induced emf e = 1 * 1.2 * 0.8* 0.6

e,mf e = 0.576 Volts

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induced current i = emf/R

i = 0.576/3

i = 0.192 Amps

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direction of current is CCW from lenz law

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magnetic force F = iLB

F = 0.8* 2 * 0.192

F = 0.3072 N

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