A loop of wire in the x-y plane has radius a and carries a constant current I in

Question

A loop of wire in the x-y plane has radius a and carries a constant current I in the counterclockwise direction as seen looking down on the loop. There is a uniform magnetic flux density B = B_0 x in the region of the loop. (This is an external B, not caused by the current in the loop.) What is the differential force dF on a differential piece of the loop dl? IaB_0 cos(phi) d phi(-z) IaB_0 cos(phi) d phi z IaB_0 sin(phi) d phi y IaB_0(-z) 0 Is there a net force on the loop? Yes, in the y direction No, because the directions are parallel so the cross-product is zero Yes, in the z direction Yes, in the -z direction No, because the integral over phi is zero Is there a net torque on the loop? Yes, in the - y direction Yes, in the y direction No, because there is no net force Yes, in the z direction No, because the directions are parallel so the cross-product is zero What is the magnetic moment m of the loop? la^2 z I pi a^2(-z) I pi a^2 z la^2 B_0 y 0 Find the torque on the loop la^2 B_0 z l_a^2 B_0 y l pi a^2 B_0(-y) l pi a^2 B_0 y 0

Explanation / Answer

a) zero (v) ( use right hand rule or F= ILXB)

b) (ii) No, because the direction are parallel so cross product is zero.

c) (ii) yes in the y-direction ( use T = uxB where u = IAn so after cross product get y direction )

d) (iii) I pi a^2 z ( use m = I A )

e) (iv) I pi a^2 Bo y ( use T = m xB)

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