Question

A point charge 0.2 C is placed on the
circumference of a non-conducting ring of
radius 1 m, which is rotating with constant
angular acceleration of 2 rad/s2. If ring starts
motion at t = 0, then magnetic field at the
centre of the ring at t = 10 s, is
(1) 3 x 10-7 tesla
(2) 10-7 tesla
(3) 4 x 10-7 tesla
(4) 2 x 10-7 tesla​

Answer 1

The magnetic field at the centre is

Explanation:

Given :

Charge $q = 0.2$ C

Radius of ring $r = 1$ m

Angular acceleration $\alpha =$ 1 $\frac{rad}{s^{2} }$

For finding the angular velocity,

 $\omega = \omega _{o} + \alpha t$

Where $t =$ 10 sec, $\omega _{o} = 0$

 $\omega =$ 10 $\frac{rad}{s}$

So linear velocity,

$v = r\omega$

$v = 10$ $\frac{m}{s}$

Magnetic field at center of the ring is given by,

$B =\frac{ \mu_{o} (qvr) }{4\pi r^{3} }$              ( ∵ $I = qvr$ )

Where $\mu_{o} = 4\pi \times 10^{-7}$

$B = \frac{4\pi \times 10^{-7} (2) }{4\pi }$

$B = 2 \times 10^{-7}$ T

Therefore, the magnetic field at the centre is $2 \times 10^{-7}$ T