The coil in the figure has 80 turns and a diameter of 20 cm. An external magneti

Question

The coil in the figure has 80 turns and a diameter of 20 cm. An external magnetic field perpendicular to the loop passes through a square region 10 cm times 10 cm. The magnetic field points out of the page and is increasing as shown in the diagram on the right. a) Find the emf induced in the coil at time t = 0.2 s. b) Find the magnitude and direction of the current induced in the circuit. The resistance of the coil is R = 8.0 ohm. Explain how you applied Lenz's law and the right hand rule to find the direction of the induced current. Use epsilon = 5 V if you did not solve a). c) What is the emf in the coil at t = 0.50 s?

Explanation / Answer

a) emf = d(flux)/dt

emf = AdB/dt

from the graph the slope is dB/dt

so dB/dt = 1/0.2 = 5 T/s

emf = 3.14*0.1^2*5 = 0.157 V

b) here filed is out of page from the right hand thumb rule thumb gives the direction of field and curl of the fingers give the direction of current

so induced current is in the counter clock wise direction

from ohms lae

v = iR

i = 5/8 = 0.625 A

c) emf = 3.14*0.1^2*2/0.5 = 0.126 V

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