Question

Calculate work done in moving a point charge ‘q’ through a distance ‘d’ along perpendicular bisector of an electric dipole, which consists of two-point charges −Q and +Q separated by a distance ‘L’.

Answer 1

An electric dipole consists of two equal and opposite charges, −Q and +Q, separated by a distance L. The perpendicular bisector (also known as the equatorial line) is the locus of points equidistant from both charges.

V = V_+Q + V_−Q

At any point on this line, the electric potential (V)  is the sum of the potentials due to each charge:

= `1/(4piε_0) (-Q)/r`

= 0

Since the potential is zero at every point on the perpendicular bisector, it is an equipotential line.

The work done Win moving a charge q between two points is given by the product of the charge and the potential difference ΔV between those points:

W = qΔV

= `q(V_"final" − V_"initial")`

Since the potential at both the initial and final positions on the perpendicular bisector is zero:

ΔV = 0 − 0

= 0

W = q × 0

= 0