Positive charge knows how to dance !

Electricity and Magnetism Level 3

Two equal negative point charges each having magnitude q are fixed at $(0,a),(0,-a)$ respectively. A uniform positive point charge $Q$ is released from rest from point $(x,0)$ where $x$ Is very very small as compared to $a$ . Then positive charge performs simple harmonic motion, then find the time period of this S.H.M.

If the answer can be represented in this form

$T= \sqrt{\frac{b\pi^3 m\epsilon_{0}a^3}{Qq}}$

Then find the value of $b$ .

The answer is 8.

1 solution

Ayon Ghosh
Oct 6, 2017

The force on the charge $Q$ will be

We can see that by symmetry $F_y = 0$ and so the expression for $F_{net,restoring}$ is :

Were we carried out the approximation for the case where $x << a$ we have $(a^2+x^2)^{3/2}$ $=$ $a^3$ .

Now clearly this equation represents $F = -kx$ indicating SHM.

Hence expression for time period is :

Hence $\beta$ $=$ $8$

Nice Solution!

Md Zuhair - 3 years, 2 months ago