What is the torque on an electric dipole in an electric field?

AI Thread Summary
The net force on an electric dipole in an electric field is calculated to be F = Q²d/(4πε₀R³). The force direction is counter-clockwise, as the left charge is repelled while the right charge is attracted towards the central charge. The discussion includes confusion regarding the calculation of torque on the dipole, which is defined as τ = p × E. Clarification is sought on how to approach the torque calculation. Understanding the relationship between the dipole moment and the electric field is essential for solving the torque problem.
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Homework Statement


A charge Q is fixed at the centre of a train track, radius R. An electric dipole with charges Q, -Q, separated by distance d. Show that the net force on the dipole is given by F = Q2d/(4πε0R3)

b) What direction is this force?
c) What is the torque on the dipole?

Homework Equations


F = (1/4*π*ε0) * (Qq/R2)
F = qE+-qE-

The Attempt at a Solution


sinθ = d/2R

F = (Q*Q / 4*π*ε0R2) (d/2R) - (-Q*Q / 4*π*ε0R2) (d/2R)

F = (Q2 d / 8*π*ε0R3) + (Q2 d / 8*π*ε0R3)

F = (2*Q2 d / 8*π*ε0R3)

F = Q2 d / (4*π*ε0R3)

b) The direction of the force is in the counter-clockwise direction (CCW). The charge on the left side of the dipole is repulsive, so it points away from the charge in the middle, while the charge on the right side is attractive, so it points towards the charge. The net force is then pointed towards the left.

c) I'm a bit lost with c) and I'm not really sure where to start. Any guidance would be much appreciated. :)
 

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What is the triangle for?
 
The torque on an electric dipole ##\vec{p}## in an electric field ##\vec{E}## is given by ##\vec{\tau}=\vec{p} \times \vec{E}##.
 
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