First slide

Magnetic flux and induced emf

Question

A semicircular wire of radius R is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength B. The induced emf between the ends is

Moderate

A

$B ω R^{2} / 2$
B

$2 B ω R^{2}$
C

is variable
D

none of these

Solution

We connect a conducting wire from A to C and complete the semicircular loop.
The emf in the semicircular loop is

zero be cause its magnetic flux does not change.
$∴$ emf of section APC + emf of section CQA = 0
$∴$ emf of section APC = emf of section $A Q C = 2 B R^{2} ω$

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