Name: Construction of Capacitor
Uploaded: 2019-07-19
Duration: 8 min 36 s
Description: What are the different types of capacitors? How does a capacitor get charged or discharged? Sounds like a tricky question, doesn't it? Watch the video to fin...

Question

A point-like charge $Q$ and a dipole with an electric moment $p_{el}$ are separated by a distance that is considerably larger than the arm of the dipole, with the result that the dipole may be considered as being point. The dipole's axis lies along the lines of force of the point charge. Compare the force acting on the dipole in the field of the point charge with that acting on the point charge in the field of the dipole.

Accepted Answer

A point dipole oriented along the lines of force of the field created by a point charge is under a force

$p_{el}$

Since the electric field created by a point charge is

$E_{Q} = \frac{Q}{4 {πε}_{0} 8 r^{2}},$

we can write

$\frac{d E_{Q}}{d r} = - \frac{Q}{2 π ε_{e} ε r^{3}},$

with the result that the force acting on the dipole is

$F_{p} = - \frac{Q p_{el}}{2 π ε_{0} ε r^{8}} .$

At points that lie on the axis of the point dipole, the electric field of the dipole is $E_{p} = \frac{p_{el}}{2 π ε_{0} ε r^{3}} .$

When a point charge $Q$ is in this field, the force acting on it is

$F_{Q} = \frac{Q p_{e l}}{2 π ε_{0} ε r^{3}} .$

In accordance with Newton's third law, this force must coincide in magnitude with, but be opposite to, force $F_{p}$ .

The positive direction in the figure accompanying the problem is the one from the point charge to the dipole. Therefore, the "minus" sign in the force acting on the dipole implies that this force is directed toward the point charge. The field created by the dipole at the point where the point charge is positioned has a "plus" sign, that is, is directed toward the dipole. The force acting on the point charge points in the same direction.

Important Questions on Electrostatics

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