Question

a charge Q is to be divided on two objects....

Answer 1

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

Answer:

Charge should be divided equally on the objects.

Explanation:

Given,A charge Q is to be divided in 2 two small objects.

To find: What should be the value of the charge on the objects so that the force between the objects will be maximum.

Solution:

For force to be maximum, dF / dq must be 0.

Let's find the force assuming that charges are Q and (Q-q).

Force can be given as:

F = kq(Q-q) / r²

Now, dF / dq = 0

or, d ( kqQ/r² - kq²/r²) = 0

or, kQ/r² - 2kq/r² = 0

or, q = Q/2

Therefore, Charge should be divided equally on the objects.