The figure shows a uniform. 1.6 T magnetic field that is normal to the Pane of a

Question

The figure shows a uniform. 1.6 T magnetic field that is normal to the Pane of a conducting coil of 20 turns with a resistance of 25 ohm and a radius of 3.0 cm. 1 he magnetic field is directed into the paper as shown. What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.2 s? What is the average current [magnitude and direction (cw or ccw)] around the loop if the magnitude of the magnetic field is doubled in 02 s? If the magnetic field is held constant at 1.6T and the loop is pulled out of the region that contains the field in 0.15 s. what is the magnitude of the average induced emf in the loop?

Explanation / Answer

a) induced emf E= pi r2 dB/dt = 3.14 x (0.03m)2 x 1.6/0.2 =2.826x10-3 x8 = 2.2608x10-2 V = 22.608 mV=0.0226V

(here r=3.0 cm = 0.03m)

b) Find the emf, E , induced in the loop. Then the current is , E/R (R = resistance)

I=E/R= 0.0226V/25 = 9.0x10-4 A (we find E in above ans a)

The magnetic field produced by the induced current should oppose the doubling of the field, therefore it should point into the page. The current should flow clock-wise

c) The induced e.m.f. is |E|=????/?t??=|?(B?A)|/?t= (1.6 x 3.14 x (0.03m)2) / 0.15 = 0.030144 V = 3.0x10-2 V

The magnetic field produced by the induced current should oppose the disappearance of the field, therefore it should point out of the page. The current should flow counterclock-wise

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