A current carrying wire is in the shape of an equilateral triangle of edge lengt

Question

A current carrying wire is in the shape of an equilateral triangle of edge length 4.0 cm. The triangle lies in the z 0 plane. The wire carries a current of 3.2 A. A current carrying wire is in the shape of an equilateral triangle of edge length 4.0 cm. The triangle lies in the z = 0 plane. The wire carries a current of 3.2 A (a) What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.22 T that points in the +z direction? N m N.m (b) What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.22 T that points in the +x direction? N-m

Explanation / Answer

Here ,

a)

area of loop , A = sqrt(3)*a^2/4

A = sqrt(3) * 0.04^2/4

A = 6.92 *10^-4 m^2

magnitude of torque = A * I * B * sin(0)

magnitude of torque = 0 N.m

b)

for +x direction

magnitude of torque = A * I * B * sin(theta)

for +x direction , as the Area vector is perpendicular to the loop .

angle between B and area , theta = 90

magnitude of torque = 6.92 *10^-4 * 0.22 * 3.2

magnitude of torque = 4.88 *10^-4 N.m

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