Question

Two positive point charges are a fixed distance apart. The sumof their charges is QT. What charge must each have inorder to (a) maximize the electric force between them, and (b)minimize it?

Answer 1

Answer:

(A) both charge should be equal (b) one charge should be zero and is $Q_T$

Explanation:

We have given the sum of charges is $Q_T$

Let one charge is q then other charge will be $Q_T-q$

According to coulombs law the force between the charges is given by

$F=\frac{K(Q_T-q)q}{r^2}$

As q is variable as it changes so differentiate with respect to q

$\frac{dF}{dq}=\frac{K}{r^2}\times (Q_T-2q)$

For maximum electric force $\frac{dF}{dq}=0$

So $Q_T=2q$

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

So for maximum force both the charge should be equal

(b) The minimum force will be the zero force for this one charge should be zero and one is $Q_T$