# Maximum Torque in Dipoles (electrostatics)

1. Feb 9, 2016

### kiwibird4

In a --specifically uniform electric field-- (I may be wrong here) my understanding is that the dipoles will result in no net dipole force (due to cancelling out) but there will actually be a net torque experienced about the center. This torque will be trying to turn the dipole so the moment, p, is parallel to the uniform electric field. From this, we see that the torque is at a maximum when theta equals pi/2, while the potential energy is at a maximum when theta=pi which is 180 degrees from the equilibrium position which is when theta= 0 and torque is 0 there.

I am wondering why (not mathematically but conceptually--I understand the sines equaling zero and cosines equaling zero aspect), if equilibrium position is supposed to be at theta equals 0 due to a net 0 torque here, why theta equals pi would not be considered an equilibrium position since the torque would be zero there as well.

Additionally, I do not quite understand why the potential energy would be zero where the torque is a maximum or theta pi/2 (I understand the mathematical reason ->cos pi/2=0 but not the conceptual reason). Wouldn't there still be some potential energy since the theta=pi/2 position is not in the equilibrium position, so there would still be a torque trying to turn the dipoles parallel to the e field and thus still some potential energy ready to turn into kinetic energy for turning the dipoles

So overall my questions are:::::
(a)why equilibrium position is only considered to be at theta=0 and not theta=pi since both have zero torque and a p parallel to e field
(b)why potential energy is considered to be zero when torque is at a max
(c)why torque's max is pi/2 if the equilibrium position is theta=0 (because then wouldn't the dipole always want to rotate towards the theta=0 position even at theta=pi, having the largest rotation at theta=pi and not theta=pi/2)

2. Feb 10, 2016

### Mario Doss

As I understood from the first question (a)........when we say that theta equals zero that will result in zero torque acting on the rectangular coil( as example) we actually measure the angel between the dipole moment (which is the perpendicular to the coil plane) and the direction of magnetic flux lines so in this case the plane of the coil is actually in 90 dgrees with the direction of magnetic field while the dipole moment is parallel to the magnetic flux lines (zero degrees)

3. Feb 11, 2016

### Aniruddha@94

a) theta= pi is also an equilibrium position ( an unstable one). Look it up if you're not familiar with the concept of equilibrium.
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b) At theta=pi/2 the potential energy is zero and the torque is maximum. But you should never try to explain things using the value of potential energy at a single point, you should always think about the change in potential energy. The slope of U ( potential energy) tells us about the force ( or torque) on a body.. Try to plot U=-pE*cos(theta) and think about it.
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c) It's true that the largest rotation happens from theta=pi ( and not pi/2).. But does that mean that the torque is maximum at theta=pi ? .. Torque is how much ' twist' acts on the body, not how much it rotates..