A loop of wire has a radius of 2.0 cm and is in a constant magnetic...

A loop of wire has a radius of 2.0 cm and is in a constant magnetic field of 0.88 T directed into the plane of the paper. If the loop collapses so the radius of the circle shrinks to zero in a time of 0.35 s, a) find the magnitude of the average induced emf in the loop. b) If the loop is part of a larger circuit, in which direction does the induced current flow as the loop closes.

Solutions

Expert Solution

induced emf = - d/dt (mag flux)

mag flux = Br²

emf = d/dt ( Br²⁾ = - 2r x dr/dt

we will find dr/dt

at t=0 -> r=2 cm

at t=0.35 -> r=0

dr/dt = change in radius / time = -2/0.35 cm/s = -2/35 m/s

r=2cm = 0.02 m

B=0.88 T

putting these values in the equation of emf,

we get emf = - 2r x dr/dt

= - 2 x 3.14 x 0.02 x 2/35 V = 6.3 mV

the direction of magnetic field willl be clockwise as shown in figure. by lenz law, induced current must produce a magnetic field which is in the same direction of initial B-field to resist the decrease in flux

genius_generous answered 1 year ago

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