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 potential at all points on the z-axis, other than the origin acts along the z-axis

Answer 1

Answer: (D)

The potential 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 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 potential is scalar quantity, so the potential at all points on the z-axis, other than the origin acts along the z-axis.