Question

A charge Q is to be divided on two objects. What shouold. be the values of the charges on the objects so that the. force between the objects can be maximum?.

Answer 1

Answer:

Hello!

Let the charge on two objects be

q and (Q-q)

As you see, the net charge is still Q.

Now, F = k q(Q-q)/r^2

Where F = Force

k = 1/(4πε)

r = distance between the charges.

Now, we want maximum force.

On looking at the formula we see that the only variable quantity is q, which is in denominator.

So, for maximum F, we can try to find the maximum value of q(Q-q)

Let u = q(Q-q)

So, u = qQ - q^2

Now, for maxima, the first derivative must be zero.

So, du/dq = Q - 2q = 0

So , q = Q/2

So, Q-q = Q/2

Thus, for maximum force, the charge Q must be divided equally into two parts (i.e Q/2 and Q/2)

Answer 2

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be the values of the charges on the objects so that the. force between the objects can be maximum?. Thus, the charge shuld be divided