Consider two charges Q and q separated by a distance d . If the potential at the point p (which is in right side from both charges) is V=0 , we can conclude (one answer only):

a)no net force would act on a test charge located at P .
b)Q and q must be same sign but different magnitude.
c)the net work required to move a third charge from inifinity to point P is zero
d)Electric field at P is zero.
e)none of the above

ΔV =V(∞)-V

V(∞)=0
V=0 =>
ΔV = 0
Work of electric field = q₃ΔV=0
Answ. c)

Thank you very much

To determine the correct answer, we need to understand the relationship between potential, electric fields, and forces in the context of charges.

The potential at a point in an electric field is a measure of the work done in bringing a positive test charge from infinity to that point. The equation for potential due to a point charge is V = k(Q/r), where k is the electrostatic constant, Q is the charge, and r is the distance from the charge.

In this scenario, we have two charges Q and q separated by a distance d, and we are given that the potential at point P, which is on the right side from both charges, is V = 0.

To find the correct answer, let's analyze each option:

a) No net force would act on a test charge located at P:
This statement is not necessarily true. While the potential is zero at P, it does not imply that there is no net force acting on a test charge at that location. The electric field can still exist, and the force depends on the magnitude and direction of the electric field.

b) Q and q must be of the same sign but different magnitude:
There is not enough information to conclude the sign or magnitude of Q and q based solely on the potential being zero at point P. The charges could have the same or opposite signs, and their magnitudes can vary.

c) The net work required to move a third charge from infinity to point P is zero:
This statement is correct. If the potential at P is zero, it means that no work is required to move a test charge from infinity to that point. The potential energy is conserved in moving the charge, and hence the net work is zero.

d) Electric field at P is zero:
This statement is not necessarily true. While the potential is zero at P, the electric field can still exist and have a non-zero value. The electric field depends on the charges and their positions.

Given these explanations, the correct answer is c) The net work required to move a third charge from infinity to point P is zero.