Point of application of magnetic torque.


by anmol21
Tags: couple, magnetic field, magnetic moment ., torque
anmol21
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#1
Jul3-12, 02:41 PM
P: 3
1. The problem statement, all variables and given/known data

Hello,
When a current carrying loop (of any shape) is placed in a uniform magnetic field B , the field is given by MχB where M is the magnetic moment vector I*A where I Is current and A is the area vector. I want to know at which point or for which axis is the torque applied given by the above equation.

2. Relevant equations

ζ=MχB
M=I*A

3. The attempt at a solution
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tiny-tim
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#2
Jul3-12, 05:52 PM
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hi anmol21! welcome to pf!

if B is uniform, the resultant force will be zero, so the effect is a pure torque

so the circuit will turn about the centre of mass of whatever the circuit is fixed to (or about whatever axis that is constrained to turn around)
anmol21
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#3
Jul4-12, 04:45 AM
P: 3
Thanks tiny-tim :)

So is the magnetic torque independent of the axis chosen ?

For example , Consider a sphere with a ring attached to it , with current I in the ring , in rotational equilibrium on a rough inclined plane. The magnetic field is vertically downwards and gravity is present. So we can equate the torque due to gravity and the magnetic torque at any point . So will be the magnetic torque be same even at the point of contact of the sphere with the ground or the centre of the sphere ?

tiny-tim
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#4
Jul4-12, 04:57 AM
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Point of application of magnetic torque.


hi anmol21!

the magnetic torque of a uniform magnetic field on a circuit is a couple

it is exactly the same as a couple (or "pure moment") in mechanics: it has the same moment about any point
"a system of forces with a resultant (a.k.a. net, or sum) moment but no resultant force"

" the moment (torque) of a couple is independent of the reference point P: Any point will give the same moment. In other words, a torque vector, unlike any other moment vector, is a "free vector"."
both quotes from http://en.wikipedia.org/wiki/Couple_(mechanics)
anmol21
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#5
Jul5-12, 05:18 AM
P: 3
thanks a lot , that clears it up :)


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