Question

A metallic rod of length ' $L$ ' is rotated with an angular speed of ' $\omega$ ' normal to a uniform magnetic field ' $B$ ' about an axis passing through one end of rod as shown in figure The induced emf will be :

• A. $\frac{1}{2} B ^2 L ^2 \omega$
• B. $\frac{1}{4} BL ^2 \omega$
• C. $\frac{1}{2} BL ^2 \omega$
• D. $\frac{1}{4} B ^2 L \omega$

Answer 1

Answer: (C)

$\frac{1}{2} BL ^2 \omega$

Answer 2

The correct answer is (C) : $\frac{1}{2} BL ^2 \omega$

∫dε=∫B(ωx)dx
ε=Bω0∫L​xdx=2BωL2​