Question

If four identical charges are placed at the points $(1,0,0),(0,1,0),(-1,0,0)$ and $(0,-1,0)$, choose the correct statements.

• 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


Let charge be $q$ at (1, 0, 0), (0, 1, 0),(-1, 0, 0) and (0, -1, 0),

At Origin:
Electric field due to charges at origin have equal magnitude but directions are as shown.
So, $E_0=0$
Potential at origin due to each charge gets added up as potential is a scalar quantity.
$V_0=\frac{4kq}{1}$
$V_0\ne 0$

At a point $P$ on $z-$ axis at a distance of $r$ from each charge:

$V_p=\frac{4kq}{r}\ne 0$

Due to symmetry components of electric field perpedicular to z-axis cancel out. So, $E_p$ is along z-axis.