Question

A charge Q is to be divided into two parts, labeled 'q' and 'Q-q? What is the relationship of q to Q if, at any given distance, the Coulomb force between the two is to be maximized?

Answer 1

Step-by-step explanation:

The two charges are q and Q - q. Let the distance between them is r

Use the formula for coulomb's law for the force between the two charges

`F = (Kq_(1)q_(2))/(r^(2))`

So, the force between the charges q and Q - q is given by

`F = \frac{K\left ( Q-q \right )q}}{r^(2)}`

For maxima and minima, differentiate the force with respect to q.

`(dF)/(dq) = (k)/(r^(2))* \left ( Q - 2q \right )`

For maxima and minima, the value of dF/dq = 0

So, we get

q = Q /2

Now
`(d^(2)F)/(dq^(2)) = (-2k)/(r^(2))`

the double derivate is negative, so the force is maxima when q = Q / 2 .