Question

A long straight vertical wire carries an upward of I_1 = 10 A. A rectangular coil of wire is located near the vertical wire as shown in the figure at right. If a = 10 cm, b = 30 cm, c = 50 cm, and I_2 = 5 A. What is the net force on the rectangular coil due to the magnetic field of the straight line?
Need help on how to solve this problem (3.4#1)

Answer 1

The magnetic field at AB due to current 10A in he straight wire, B(AB)=$\mu$₀ * I /2$\Pi$ r =4π × 10⁻⁷ *10/2π*0.01 =2× 10⁻⁴

Force on AB ,F=ILBsin$\Theta$ =5*0.5*2× 10⁻⁴ *sin 90=5× 10⁻⁴ N

The direction is into the paper

similarly the field at CD,   B(CD)=$\mu$₀ * I /2$\Pi$ r =4π × 10⁻⁷ *10/2π*0.03 =0.667× 10⁻⁴

Force on AB ,F=ILBsin$\Theta$ =5*0.5* 0.667× 10⁻⁴ *sin 90=1.667× 10⁻⁴ N

If we take the torque about CD 5× 10⁻⁴ N*(0.3-0.1)=10⁻⁴ N.m and tends to rotate the loop about CD into the page