A copper rod A B of length l, pivoted at one end A, rotates at constant angular velocity ω, at right angles to a uniform magnetic field of induction B. The emf, developed between the mid point C of the rod and end B is

Question

A copper rod A B of length l, pivoted at one end A, rotates at constant angular velocity ω, at right angles to a uniform magnetic field of induction B. The emf, developed between the mid point C of the rod and end B is (A) (B ω l2/8) (B) (3/4) B ω l2 (C) (B ω l2/4) (D) (3/8) B ω l2

Tardigrade Admin · Accepted Answer

ε=∫ limits1 / 21 B ω x d x =B ω((x2/2))1 / 21 =(B ω/2)(l2-l2 / 4) =(3/8) B ω l2

Q. A copper rod $A B$ of length $l$ , pivoted at one end $A$ , rotates at constant angular velocity $ω$ , at right angles to a uniform magnetic field of induction $B$ . The emf, developed between the mid point $C$ of the rod and end $B$ is

$\frac{B ω l ^{2}}{8}$

$\frac{3}{4} B ω l^{2}$

$\frac{B ω l ^{2}}{4}$

$\frac{3}{8} B ω l^{2}$

$ε = 1/2 \int 1 B ω x d x$
$= B ω (\frac{x ^{2}}{2})_{1/2}^{1}$
$= \frac{B ω}{2} (l^{2} - l^{2} /4)$
$= \frac{3}{8} B ω l^{2}$

Q. A copper rod AB of length l, pivoted at one end A, rotates at constant angular velocity ω, at right angles to a uniform magnetic field of induction B. The emf, developed between the mid point C of the rod and end B is

8Bωl2​

43​Bωl2

4Bωl2​

83​Bωl2