Question

If $E_a$ be the electric field intensity due to a short dipole at a point on the axis and $E_r$ be that on the right bisector at the same distance from the dipole, then

• A. $E_a=E_r$
• B. $E_a=2E_r$
• C. $E_r=2E_a$
• D. $E_a=\sqrt{2}{E}_r$

Answer 1

Answer: (B)

$E_a=2E_r$

If $q$ be the charge on one point of the dipole and the half length is equal to $d$,
then the total dipole moment is given by, $p$ = $2qd$
If $E_a$ be the field at any axial point, then it is given by $\frac{kp}{r^3}$
Similarly, the field at any point on the right bisector is given $E_r=\frac{kp}{2r^3}$
Hence, $E_a=2E_r$