Torque on a coil at an angle to a uniform magnetic field

[qazxsw11111]

Hi everyone. I have a confusion over a certain concept. I know the torque for a rotating coil in a uniform magnetic field is BIAN. But what if the coil is at a certain degree to the magnetic field?
http://img44.imageshack.us/img44/1926/magnetic.th.png

Sorry for the bad drawing.

My interpretion:
Ok, so the current is still perpendicular to the B-field (into/out of paper), even if there is an inclination. The formula should still be BIAN right?

Assessment Book answer:
If the magnetic field is uniform, the component of B which is effective is Bcosα, and torque=(Bcosα)IAN. [WHY?]

Further question: Whats the difference between a radial magnetic field and a uniform magnetic field?

Thanks. Just a little confused since this is a new topic for me.

EDIT: Typo errors.

 

[kuruman]

The net force on the current loop is zero if the magnetic field is uniform. However, the net torque may or may not be zero depending on the orientation of the loop. If the magnetic field lines are in the plane of the loop, the torque will be zero. If the magnetic field lines are perpendicular to the plane of the loop, The torque will have its maximum value BIAN.

Take a book and place it flat on the table in front of you. Grab the right edge with your right fingers and the left edge with your left fingers. Pull with equal force. The book will not move and will not turn. Now place the book standing up in one edge. Push the bottom to the left with one hand and the top to the right. Even without gravity the book will turn, but its center of mass will stay in place. There is a net torque but not a net force.

I have never heard of a radical magnetic field. Perhaps someone else has. A uniform magnetic field has the same magnitude and direction at every point in space.

 

[Chi Meson]

"Radical" was supposed to be "radial" perhaps? That would be the same as diverging from a point, getting weaker as distance increases. Magnetic field lines cannot diverge from a point (Gauss' Law) but I suppose in one locality they can be diverging.

 

[qazxsw11111]

Thanks for the reply. Yes, it is radial (cancel out the c). Must have typed too fast...

Ok, I sort of figured it own on my own. The BIAN formula is derived from BIL x distance between the two arms x N. The current that generates a torque is always either in or out of the paper (diagram above) so that there can be a up/down force to generate a torque about the centre axis (perpendicular to paper). So the current will always be perpendicular to the plane of the paper.

When calculating the torque, we need to take the force that is perpendicular to the wire joining the two arms and resolving, there will be a Fcosα, which subbing back into equation, is BIANcosα.

Is this correct? Thanks.

 

[kuruman]

That is correct. The statement I made in my first posting is incorrect. It should read

However, the net torque may or may not be zero depending on the orientation of the loop. If the magnetic field lines are in the plane of the loop, the torque will have its maximum value BIAN. If the magnetic field lines are perpendicular to the plane of the loop, the torque will be zero.

Your angle α is defined between the magnetic field lines and the plane of the loop. A more conventional definition is the angle between the field lines and the normal to the loop. In this case the cosine becomes a sine. I am mentioning this just in case you come across a reference that uses this convention.