Question

A uniform magnetic field of induction $B$ is confined in a cylindrical region of the radius $R$ . If the field is increasing at a constant rate of $\frac{d B}{d t}=\alpha \, Ts^{- 1}$ , then the intensity of the electric field induced at a point $P$ distant $r$ from the axis as shown in the figure is equal to

• A. $\frac{1}{8}r$
• B. $\frac{1}{8}r\alpha $
• C. $\frac{1}{2}r\alpha $
• D. $r$

Answer 1

Answer: (C)

Magnetic flux linked with circular section of radius $r$ of the cylinder , $\phi=\left(\pi r^{2}\right)B.$

Due to this induced emf, an electric field E is established which is equal to potential difference per unit length.
$E=\frac{e}{2 \pi r}=\frac{\pi r^{2} \alpha }{2 \pi r}$
$E=\frac{1}{2}r\alpha $