A uniform and constant magnetic field B is directed perpendicularly into the plane of the page everywhere within a rectangular region as shown above. A wire circuit in the shape of a semicircle is uniformly rotated counterclockwise in the plane of the page about an axis A. The axis A is perpendicular to the page at the edge of the field and directed through the center of the straight-line portion of the circuit. Which of the following graphs best approximates the emf ε induced in the circuit as a function of time t?
(GR9277 #57)
Solution:
Faraday's Law: ɛ = − dΦ/dt
with Φ = NBA
Given:
N = 1,
B constant
A increases and decreases uniformly since the wire circuit rotates uniformly
→ the rate of change of A, dA/dt = constant.
ɛ = − BdA/dt = constant
Only graph (A) shows constant ε.
ε changes periodically from positive to negative since only half of area covered in magnetic field.
Answer: A
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