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 suits at a magnitude of B = 0.1 T and increases at a rate of 0.6 T/s. What is the magnetic flux, phi_H, at the beginning when B = 0.1T? What is the voltage induced in the loop? What current flows through the loop due to the induced voltage? Does the current flow CLOCLWISE or COUNTERCLOCKWISE? When the external magnetic field is at B = 2T, 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

h =0.8 m ,w =1.2 m ,R =3 ohms, B =0.1 T, dB/dt =0.6 T/s

(a) Magnetic flux phi = B.A = 0.1*0.8*1.2= 0.096 T.m^2

(b) from faradays law induced emf = -d(phi)/dt = -AdB/dt

V = -0.8*1.2*0.6 = -0.576 V

From ohms law V = iR

i = 0.576/3 = 0.192 A

(c) From fleming right hand rule current flow is clockwise direction

e) L =0.8 m , B = 2T , i =0.192 A

Magnetic force F = iLB = 0.192*0.8*2

F = 0.3072 N

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