There is a magnetic field of strength B=5 T, pointing into the page. Imagine a b

Question

There is a magnetic field of strength B=5 T, pointing into the page. Imagine a bendable loop of wire of total length 4 meters. Assume that there is a 1000 W resistor in the wire. Initially, the wire is bent into a circle (so that the length is its circumference). Then, it is magically deformed into a square. During this deformation, which takes 1 second, find the magnitude & direction (clockwise/counterclockwise) of the current induced in the wire. Does the loop of wire experience a torque? Why or why not?

Explanation / Answer

initially radius of the loop, r = L/(2*pi)

= 4/(2*pi)

= 0.634 m

Area of the loop, A1 = pi*r^2

= 1.27 m^2

when the loop becomes square

lengh of each side = 1 m

so, Area of the loop, A2 = 1^2 = 1 m^2

induced emf = B*dA/dt

= 5*(1.27-1)

= 1.35 volts

induced current, I = emf/R

= 1.35/1000

= 1.35*10^-3 A

Direction: clockwise

Beacuse the area of the loop is decreasing so magnetic flux through the loop decreases.

According to Lenz's law this induced current should be clockwise

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