A copper rod of length L rotates at an angular velocity ω in a uniform magnetic field B as shown. What is the induced emf across the ends?

Question

A copper rod of length L rotates at an angular velocity ω in a uniform magnetic field B as shown. What is the induced emf across the ends? (A) (1/2) ω B L2 (B) (1/3) ω B L2 (C) (1/2) ω B L3 (D) (1/4) ω B L2

Tardigrade Admin · Accepted Answer

Induced emf for element on the rod d e=B v d L sin 90°=B v d L Net emf, e=∫ d e=∫ limits0L B v d L=∫ limits0L B r ω d L=((B r2 ω/2))0L

Q. A copper rod of length $L$ rotates at an angular velocity $ω$ in a uniform magnetic field $B$ as shown. What is the induced emf across the ends?

$\frac{1}{2} ω B L^{2}$

$\frac{1}{3} ω B L^{2}$

$\frac{1}{2} ω B L^{3}$

$\frac{1}{4} ω B L^{2}$

Induced emf for element on the rod
$d e = B v d L sin 9 0^{\circ} = B v d L$
Net emf, $e = \int d e = 0 \int L B v d L = 0 \int L B r ω d L = (\frac{B r ^{2} ω}{2})_{0}^{L}$

Q. A copper rod of length L rotates at an angular velocity ω in a uniform magnetic field B as shown. What is the induced emf across the ends?

21​ωBL2

31​ωBL2

21​ωBL3

41​ωBL2