The figure shows a stationary conductor whose shape is similar to the letter c.

Question

The figure shows a stationary conductor whose shape is similar to the letter c. The radius of Its circular portion Is a 20.0 cm. It IS placed In a constant magnetic field of 0 70 T directed out of the page. A straight conducting rod, 20.0 cm long. Is pivoted about point O and rotates with a constant angular speed of 1 40 rad/s. Determine the induced emf in the loop POQ. Note that the area of the loop is theta s^2/2. If all the conducting material has a resistance per length of 5.00 omega/m, what is the induced current in the loop POQ at the instant 0.250 s after point Q.

Explanation / Answer

given data
a=20cm
B = 0.70T
rod length = 20cm
angular speed = 1.40 rad/s
resistance/length = 5 ohm/m
t = 0.250 s

a)
= -d/dt

= B A
d/dt = B dA/dt (B is constant)

A = (1/2)r²
dA/dt = (1/2)r²(d/dt) (r is constant, as is d/dt)
dA/dt = (1/2)r²()

= -(1/2)Br²()
= -(1/2)(0.7 T)(0.20 m)²(1.40rad/s)
= -0.098 V

b)
There 's no information here about the conducting rod at t = 0 (initial position).
If it starts from OQ,
= t
= (1.40 rad/s)(0.250 s)
= 0.35 rad

L = 2r + r
L = r(2 + )
L = (0.20 m)(2 + 0.35 rad)
L = 0.47 m

R = (0.47 m)(5 /m)
R = 2.35

V = IR
0.098 V = I(2.35 )
I = 0.0417 A or 41.7mA

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