A rectangular loop of wire is ? = 800 mm long and w = 500 mm wide. You bend the

Question

A rectangular loop of wire is ? = 800 mm long and w = 500 mm wide. You bend the ? sides into a semicircle while keeping the w sides straight, as shown in (Figure 1) , and then move the curved loop at speed v = 0.900 m/s into a uniform magnetic field of magnitude B = 0.300 T . One of the sides labeled w is the leading edge of the moving loop, and the magnetic field direction is perpendicular to the plane CDEF.

A)

What is the value of the emf induced in the loop?

Express your answer with the appropriate units. Enter positive value if the emf causes induced current in the direction CDEF and negative value if the emf causes induced current in the direction CFED.

B)

What is the induced emf if the loop is rotated 90? in the plane CDEF so that the side leading into the magnetic field is one of the curved sides?

Express your answer with the appropriate units. Enter positive value if the emf causes induced current in the direction CDEF and negative value if the emf causes induced current in the direction CFED.

Explanation / Answer

Here,

l = 800 mm = 0.8 m

W = 0.5 m

v = 0.90 m/s

B = 0.30 T

part A)

for the value of emd induced in the loop is E

E = B * v * W

E = 0.30 * 0.90 * 0.5 V

E = 0.135 V

the value of emf induced is 0.135 V

Using Lenz's law

the direction of current is D to C

the direction of current is CFED

part B)

let the radius of semicircle is r

l = pi * (r)

r = 0.8/pi = 0.255 m

induced emf = B * v * 2r

induced emf = 0.30 * 0.90 * 2 * 0.255

induced emf = 0.138 V

the induced emf in the loop is 0.138 V

Using Lenz's law

the direction of current is E to D

the direction of current is CFED

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