Q. 133.8( 11 Votes )

# (a) Draw the equipotential surfaces corresponding to a uniform electric field in the z-direction.

(b) Derive an expression for the electric potential at any point along the axial line of an electric dipole.

Answer :

(a)

Note that the electric field is always perpendicular to the equipotential surface. Hence, the equipotential surfaces are going to be infinite plane sheets parallel to the x-y plane.

Also, the electric field strength is proportional to the distance between the surfaces. Hence, the surfaces will be evenly spaced.

(b)

Let charge *+q* and *-q* be separated by distance *2a*. Let origin be at the centre of the two charges. Consider any arbitrary point P (x,0).

Let r_{a} be the distance of point P from the positive charge and r_{b} be the distance of the point P from the negative charge.

The electric potential at point P is given by:

We have two cases:

Case I: and

Now,

and

Case II: and

Now,

and

Case III: and

Now,

and

Case IV:

and

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A charge 'q' is moved from a point A above a dipole of dipole moment 'p' to a point B below the dipole in equatorial plane without acceleration. Find the work done in the process.

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