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

In summary: In this case, the electric field is not uniform due to the presence of the fixed charge Q at the center of the train track. Therefore, the dipole experiences a torque that is dependent on its orientation. We can use the definition of torque and the given formula for the force to determine the torque on the dipole. In summary, the net force on the dipole is given by F = Q2d/(4πε0R3) in the counter-clockwise direction, and the torque on the dipole is given by the product of the dipole moment and the electric field, which is not uniform in this case.
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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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  • #2
What is the triangle for?
 
  • #3
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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1. What is the definition of net force on a dipole?

The net force on a dipole is the overall force acting on a dipole, which is a pair of equal and opposite charges separated by a small distance. It takes into account both the strength of the electric field and the orientation of the dipole.

2. What factors contribute to the net force on a dipole?

The net force on a dipole is influenced by the strength of the electric field, the magnitude of the charges on the dipole, and the distance between the charges. It is also affected by the orientation of the dipole with respect to the direction of the electric field.

3. How do you calculate the net force on a dipole?

The net force on a dipole can be calculated using the formula F = qEsinθ, where F is the force, q is the magnitude of the charge, E is the strength of the electric field, and θ is the angle between the dipole and the electric field.

4. How does the net force on a dipole change with distance?

The net force on a dipole decreases with distance. As the distance between the charges increases, the electric field strength decreases, resulting in a weaker force on the dipole.

5. Can the net force on a dipole be zero?

Yes, the net force on a dipole can be zero if the dipole is aligned parallel to the electric field. In this case, the angle between the dipole and the electric field is zero, resulting in a sine of zero in the formula for calculating the net force.

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