Question

A current carrying wire is in the shape of an equilateral triangle of edge length 4 cm. The triangle lies in the z = 0 plane. The wire carries a current of 2.2 A.

1)

What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.32 T that points in the +z direction?
N·m

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2)

What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.32 T that points in the +x direction?

Answer 1

given
L = 4 cm = 0.04 m
I = 2.2 A
B = 0.32 T

1)
Area of equilateral triangle, A = sqrt(3)*L^2/4

= sqrt(3)*0.04^2/4

= 6.93*10^-4 m^2

magnetic dipole moment of the loop, M = I*A

= 2.2*6.93*10^-4

= 1.52*10^-3 A.m^2

Torque acting on the loop, T = M*B*sin(theta) (here theta is the angle between normal to the loop and B)

= 1.52*10^-3*0.32*sin(90)

= 4.86*10^-4 N.m <<<<<<<<-----------Answer

2) Torque acting on the loop, T = M*B*sin(theta)

= 1.52*10^-3*0.32*sin(0)

= 0 N.m <<<<<<<<-----------Answer