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Chapter 22: Problem 13

Two equal but opposite charges form a dipole. Describe the equipotential surface on which \(V=0\)

Short Answer

Expert verified
The equipotential surface on which \(V=0\) for a dipole is a plane that is perpendicular to the line joining the two charges and lies exactly in the middle of them.

Step by step solution

01

Understanding the Dipole

A dipole consists of two equal but opposite charges, with \(+q\) and \(-q\) respectively, separated by a distance \(d\). The potential at a point, due to a positive charge, is \(kq/r\) where \(k\) is Coulomb's constant and \(r\) is the distance from the charge to the point. Similarly, the potential due to the negative charge is \(-kq/r\). The net potential at a point is the sum of the potential due to the positive charge and the potential due to the negative charge.
02

Setting the Total Potential Equal to Zero

The equipotential surface is where the total potential of the system at every point is the same. To find where the total potential is zero, we set this sum equal to zero: \(kq/r - kq/r = 0\). Here, \(r_1\) is the distance from the positive charge to the point and \(r_2\) is the distance from the negative charge. Hence the equation becomes \(r_1 = r_2\).
03

Describing the Equipotential Surface

For the distances \(r_1\) and \(r_2\) to be equal, the point must lie in a plane perpendicular to the line joining the two charges and lying exactly in the middle of them. This plane is the equipotential surface for which \(V=0\).

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Most popular questions from this chapter

A solid sphere contains positive charge uniformly distributed throughout its volume. Is the potential at its center higher than, lower than, or the same as at the surface?

What's the potential difference between the terminals of a battery that can impart \(7.2 \times 10^{-19} \mathrm{J}\) to each electron that moves between the terminals?

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