Two point charges,one q and the other -q,form a dipole separated by a distance d.A third charge Q is placed midway between these two charges.If the distance between q and -q is then doubled with the Q staying midway between the other two,what happens to the force on Q?
A)It halves.
B)It reduces by a factor of 8.
C)It stays the same.
D)It quarters.

Question

Two point charges,one ​q and the other -q,form a dipole separated by a distance d.A third charge Q is placed midway between these two charges.If the distance between q and -q is then doubled with the Q staying midway between the other two,what happens to the force on Q?
A)It halves.
B)It reduces by a factor of 8.
C)It stays the same.
D)It quarters.

Quizplus · Accepted Answer

The force on charge Q due to the dipole (q, -q) can be described by the formula:

F = (1/4πε) [(q/r1^2 - q/r2^2) * d]

where ε is the permittivity of free space, r1 and r2 are the distances from Q to q and -q respectively, and d is the separation between q and -q.

When the distance between q and -q is doubled, the separation d in the above formula also doubles. Therefore, the force on Q becomes:

F' = (1/4πε) [(q/(2r1)^2 - q/(2r2)^2) * 2d]

Simplifying this expression, we get:

F' = (1/4πε) [(q/r1^2 - q/4r2^2) * 2d]

Notice that the second term in the bracket becomes smaller by a factor of 4, since the distance r2 is doubled. Therefore, the new force F' is:

F' = F/2

In other words, the force on Q is reduced by a factor of 2, or it quarters. Therefore, the correct answer is D.

Two Point Charges,one ​Q and the Other -Q,form a Dipole

Two Point Charges,one Q and the Other -Q,form a Dipole