Question

Four identical charges are placed at the points (1, 0, 0), (0, 1, 0), (-1, 0, 0) and (0, -1, 0).

• A. The potential at the origin is zero.
• B. The field at the origin is zero.
• C. The potential at all points on the z-axis, other than the origin, is zero.
• D. The field at all points on the z-axis, other than the origin, acts along the z-axis.

Answer 1

Answer: (B), (D)

The correct options are
B The field at the origin is zero.
D The field at all points on the z-axis, other than the origin, acts along the z-axis.

Here the distance (r) from origin o to all charges will be equal. i.e , $r=1$
The potential at origin o is $V=k(q/r+q/r+q/r+q/r)=4kq$
As the electric field is a vector quantity. So the electric field at origin is zero because the filed will cancel each other along x and y axis.
along x axis, $E=kq/r^2-kq/r^2=0$
along y axis, $E=kq/r^2-kq/r^2=0$
As the electric field is a vector quantity, so the field at all points on the z-axis, other than the origin acts along the z-axis.