Question

Two point charges are at x=0 and x=L, respectively, and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium. What are the magnitude, sign, and x-coordinate of the third charge.

Answer 1

Answer:

Explanation:

The point will lay at x = L/2 ( in the middle)

Let the charge given be Q at x = 0 and L ,  and q is the charge required.

Force on charge put on x = 0 , due to charge in the middle

k Q q / .5 L

Force on charge put on x = 0 , due to charge at x = L

= k Q q /  L

Total force

= k Q q / .5 L  + k Q² /  L  = 0,  FOR BALANCE.

2q = - Q

q = - Q / 2

In the middle , half the charge of either of equal charge placed at x = 0 and L should be placed . Its nature negative .

Answer 2

Answer:

Explanation:

Let the two charges is at x = 0 an x = L is Q.

Let the third charge is q placed at x = L/2.

Let the net force on the charge placed at x = 0 is zero.

force on charge Q placed at x = 0 due to the charge Q placed at x = L

$F_{1}=\frac{KQ^{2}}{L^{2}}$

force on charge Q placed at origin due to charge q placed at x = L/2

$F_{2}=\frac{4KQq}{L^{2}}$

As the net force on the charge at x = 0 is zero so

F1 = F2

$\frac{KQQ}{L^{2}}=\frac{4KQq}{L^{2}}$

Q = 4 q

q = Q / 4

Charge q should be negative in nature as the system of charges is in stable equilibrium.

In the middle , half the charge of either of equal charge placed at x = 0 and L should be placed . Its nature negative .