There is a magnetic field of strength B=5 T, pointing into the page. Imagine a b
ID: 1390592 • Letter: T
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