Question

. A charge Q is divided into two parts of q and Q – q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of Q/q should be

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\frac{Q}{q} = 2$ for maximum force.

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• A charge Q is separeted into two charges q and Q-q.

☆ᴛᴏ ғɪɴᴅ☆

• The ratio $\frac{Q}{q}$ for maximum replusive force when separated by a distance.

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

By Coulomb law

$F = \frac{Kq(Q-q)}{r²}$

To calculate point of maxima of F, let us calculate dF/dq and equate it to zero

$\frac{dF}{dq} = 0$

$⇒\frac{K}{r²}\frac{d}{dq}[q(Q-q)] = 0$

$⇒q(-1) + 1.(Q-q)= 0$

$⇒Q-2q= 0$

$⇒q= \frac{Q}{2}$

Now,

$\frac{d²F}{dq²} =\frac{K}{r²}\frac{d}{dq}[Q-2q]$

$⇒\frac{d²F}{dq²} =-\frac{2K}{r²}$

$⇒\frac{d²F}{dq²} < 0$

Hence $q= \frac{Q}{2}$ is a point of maxima

Therefore

$q= \frac{Q}{2}$

$⇒\frac{Q}{q} = 2$