A teacher models a polar molecule by two charges, and , held apart. This is much larger than a real molecule, but it keeps the numbers simple. The figure shows two situations.
In the left panel, P lies on the axis of the dipole and Q lies on its equatorial line, and each is from the centre O. This distance is much larger than the separation of the charges, so you may use the formulae for a short dipole. In the right panel, the same dipole sits in a uniform external field of magnitude , with its dipole moment at to the field. Take .
Decide which of P and Q has the stronger field before you calculate, and watch the sign of the work.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , separation , , .
(a) Dipole moment. .
(b) On the axis. , with . Here and , so .
(c) On the equatorial line. , half of the field on the axis. It points opposite to .
(d) Torque. .
(e) Work. , so . The work is positive: the agent works against the field.
Answer: (a) . (b) . (c) . (d) . (e) .
Check. The exact fields of the two charges at are on the axis and on the equatorial line, the same to one decimal place. So the short-dipole formulae are good here.
Watch out. The ratio of the two fields is , whatever the distance. If you use you get , a negative number: that is the work done by the field, not by the agent.
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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.