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A dipole (whose moment has magnitude \(p\) ) is placed a distance \(r\) from an infnite line charge with uniform charge density \(\lambda\) so that the dipole moment \(\vec{p}\) is parallel to the infinite line of charge. The dipole is fixed in place but is free to rotate and further the dipole distance \(d\) is very small compared to \(r\).

(a) What is the magnitude of the torque exerted on the dipole? Which way does it start to rotate?

(b) What is the maximum rotational kinetic energy that the dipole attains due to the field? Assume there are no other forces present.

(c) Now suppose that the dipole is rotated so that its potential energy is minimized but is otherwise stationary. What is the total force on the dipole? 

Hint:

Treat the dipole as two charges separated by a distance \(d\) and compute the net force.

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