Question

Let B be the midpoint of AC. Two point charges Q are placed at A and C. What should be the value of charge placed at B so that the system remains at equilibrium?

(a) –Q/2

(b) –Q/4

(c) +Q/2

(d) +Q/4

I have been asked this question in my homework.

My question comes from Coulomb’s Law in section Charges and Fields of Physics – Class 12

Answer 1

Right option is (b) –Q/4

For explanation I would say: Whatever the value of q be, it will undergo equal force on both sides, hence q will be steady.

Now, for stability of Q, net force on Q must be zero.

\(\frac {1}{4\pi\epsilon_o} \, \frac {Q^2}{d^2} + \frac {1}{4\pi\epsilon_o} \, \frac {Q.q}{(\frac {d}{2})^2}\) = 0

⇒ \(\frac {Q^2}{d^2} = \frac {-Q q}{\frac {d^2}{4}}\)

⇒ Q = -49 ⇒ q = –\(\frac {Q}{4}\)