Electromagnetic Induction Question 2
Question 2 - 24 January - Shift 2
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 :
(1) $\frac{1}{4} B^{2} L \omega$
(2) $\frac{1}{4} BL^{2} \omega$
(3) $\frac{1}{2} BL^{2} \omega$
(4) $\frac{1}{2} B^{2} L^{2} \omega$
Show Answer
Answer: (3)
Solution:
$\int d \varepsilon=\int B(\omega x) dx$
$\varepsilon=B \omega \int_0^{L} xdx=\frac{B \omega L^{2}}{2}$
