A single rectangular coil consists of closely spaced turns of wire
PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism
Problem
A single rectangular coil consists of N=50 closely spaced turns of wire, each turn forming a rectangle of width 0.040m and height 0.060m. The coil carries a steady current of 0.80A, with the current flowing clockwise when the coil is viewed from the right. The coil is suspended so that its plane makes an angle θ with a uniform magnetic field of magnitude 0.25T, as shown in the side-view sketch you will draw in part (a). The axis about which the coil can rotate is along its top edge.
Ignore the mass of the wire and the effect of gravity.
(a) Draw a clear side-view sketch of the coil, labeling the current direction in each side and the direction of the magnetic field. Indicate the angle θ between the plane of the coil and the magnetic field.
(b) Derive an expression for the magnitude of the magnetic force on each of the four sides of a single turn of the coil in terms of I, B, the appropriate length, and θ. State any assumptions you make.
(c) Show algebraically that the vector sum of all magnetic forces on a single turn is zero, regardless of the value of θ.
(d) Derive an expression for the magnitude of the net torque τ on the entire coil about its top edge in terms of N, I, B, the area A of one turn, and θ.
(e) If θ=30∘, calculate the numerical value of the torque on the coil.