I'm stuck on solving a linear quadrupole problem

[BREAD]

Homework Statement

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Homework Equations

I found this is about linear quadrupole and these are potential of it.

[/B]

The Attempt at a Solution

So, i solve the problem (a) by using potential.

This is what I've done, I'm not sure if it is right though.[/B]

And i have no idea how can i solve (b),(c) problems.

 

[John Park]

For part (a) I wonder if you were expected to do simple electrostatics and geometry--adding up the single-particle fields, and doing first-order calculations for the distances. (I note that in your derivation you didn't insert the unit vectors until the last steps, so technically you're equating vectors to scalars.)

For (b) I don't know what they mean by a "singular" charge density, but perhaps they're thinking of something like p-orbitals.

For (c) I think this is definitely a case of simple electrostatics and geometry. Define a uniform electric field along a general direction (by symmetry this just means defining one angle) and work out the force on each charge separately; add up the results. The torque will be related to the difference in forces on the three charges (actually only the outer two are important).