# Confusion regarding torque given by M×B

The magnetic torque acting on a loop of magnetic moment M placed in a magnetic field B, is given by τ=M×B. My question is, about which axis does this give the torque about? Is it the instantaneous axis of rotation or the axis about the centre of mass? How do we decide this axis?

Consider the following case of a cylinder(with a planar coil carrying current, plane parallel to inclined plane at the instant, the inclined plane making an angle θ with the horizontal) rolling down an incline such that the net torque on it is 0 , now, in this case will the torque given by M×B be about the point of contact with the inclined plane? Or will it be about the Centre of mass of the cylinder?

The magnetic torque acting on a loop of magnetic moment M placed in a magnetic field B, is given by τ=M×B. My question is, about which axis does this give the torque about?

Note that $$\tau=M\times B$$ is an vector product, then $$\tau$$ is orthogonal to the plane of $$M$$ and $$B$$.

Is it the instantaneous axis of rotation or the axis about the centre of mass?

Torque $$\tau$$ is also orthogonal to the plane of rotation, therefore it is about the axis of rotation.

• WHICH axis of rotation. You missed the question entirely. – user226375 Apr 23 '19 at 13:26
• Im not sure if i understand the question entirely, but the torque vector $\tau$ tries align the magnetic moment vector $M$ with external $B$. Also, If you know the direction/axis of $\tau$, you know the axis of rotation. – user164843 Apr 23 '19 at 16:08
• Not necessarily. For the same direction of torque, it can have several axes. And, if you don't understand the question why bother answering – user226375 Apr 23 '19 at 16:26
• I don't understand, Torque is an entity formally defined as to be orthogonal to plane of rotation (i.e. in the rotation axis) how can the same torque have several axes? if you refer to Precession or Net torque, that's not the case. – user164843 Apr 24 '19 at 7:23
• Consider a plane. It can have infinite axes (orthogonal lines) passing through it at different points. – user226375 Apr 24 '19 at 7:34