A rectangular circuit sits in a uniform magnetic field. it has a height of h=0.8

Question

A rectangular circuit sits in a uniform magnetic field. it has a height of h=0.8m and width of w=1.2m and a resistor with R=3 ohms. 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. SHOW ALL WORK PLEASE :)

a. What is the magnetic flux at the beginning when B=0.1 T

b. what is the voltage induced in the loop

c. what current dlows through the loop due to the induced voltage

d. does the current flow clockwise or counterclockwise

e. when the external magnetic field is at B=2T what is the force on the left side (of length h=0.8m) due to the current flowing in the external magnetic field

Explanation / Answer

a) flux = BA = 0.1 x 0.8 x 1.2 = 0.096 Wb

b) voltage = d(flux)/dt = A x dB/dt = 0.8 x 1.2 x 0.6 = 0.576 V

c) current = voltage/resistance = 0.576/3 = 0.192 A

d) counterclockwise (using lenz law)

e) force = IhB = 0.192 x 0.8 x 2 = 0.3072 N toward right side.

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