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

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 (A) B ω R2 / 2 (B) 2 B ω R2 (C) is variable (D) none of these

Tardigrade Admin · Accepted Answer

We connect a conducting wire from A to C and complete the semicircular loop. The emf in the semicircular loop is zero because its magnetic flux does not change. ∴ emf of section A P C+ emf of section C Q A=0 ∴ emf of section A P C= emf of section A Q C=2 B R2 ω

Q. 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

$B ω R^{2} /2$

$2 B ω R^{2}$

is variable

none of these

We connect a conducting wire from $A$ to $C$ and complete the semicircular loop.
The emf in the semicircular loop is zero because its magnetic flux does not change.
$∴$ emf of section $A PC +$ emf of section $CQ A = 0$
$∴$ emf of section $A PC =$ emf of section $A QC = 2 B R^{2} ω$

Q. 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

BωR2/2

2BωR2