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## Homework Statement

Three metal balls with unequal radii R1 < R2 < R3 are placed at the vertices of an equilateral triangle, whose sides have length a. The balls are connected by thin metal wires. A positively charged rod is brought into contact with one of the balls and transfers an amount of charge +Q to the system.

(a)Show that the charge Qi on the i-th sphere (i = 1,2,3) is given by

[tex]\frac{Qi}{Q}[/tex]=[tex]\frac{Ri}{R1+R2+R3}[/tex]

(b)Hence show that the potential V at the centre of the triangle is given by

[tex]V=\frac{Q\sqrt{3}}{4\pi\epsilon_0a}[/tex]

(c)What is the magnitude and direction of the electric dipole moment of the system, if two of the balls have equal radii (e.g. R1 = R2)? Hint: electric dipole moments add like vectors.

## Homework Equations

[tex]V=\frac{Q}{4\pi\epsilon_0R}[/tex]

[tex]\vec{p}=q\vec{d}[/tex]

## The Attempt at a Solution

I kept trying this question,but still have no idea for part (a).

I think I have solved Part B,but I noticed the question uses "hence", does that mean part (b) should use part (a) as part of solution? But I simply subsititute everything to formula [tex]V=\frac{Q}{4\pi\epsilon_0R}[/tex],and I ended up part (b) without using Part (a),is there anything wrong with that?

Part (c) I tried to use formular [tex]\vec{p}=q\vec{d}[/tex],but I don't know what to do next.

Can anyone please help me with some details? Thanks a lot.