Question

An $\alpha$-particle is moving along a circle of radius $R$ with a constant angular velocity $\omega$. Point $A$ lies in the same plane at a distance $2R$ from the center. Point $A$ records magnetic field produced by the $\alpha$-particle. If the minimum time interval between successive times at which $A$ records zero magnetic field is $t$, the angular speed $\omega$, in terms of $t$, is :

• A. $\frac{2\pi }{t}$
• B. $\frac{2\pi }{3t}$
• C. $\frac{\pi }{3t}$
• D. $\frac{\pi }{t}$

Answer 1

Answer: (B)

$\frac{2\pi }{3t}$

Point $A$ shall record zero magnetic field when the $\alpha$-particle is at positions $P$ and $Q$ as shown in figure.
The time taken by $\alpha$-particle to go from $P$ to $Q$ is :
$t=\frac{T}{3}=\frac{1}{3}\times \frac{2\pi }{\omega }or\omega =\frac{2\pi }{3t}$