In the figure a long straight wire carries a current i1 293

In the figure, a long straight wire carries a current i_1 = 29.3 A and a rectangular loop carries current i_2 = 21.7 A. Take a = 1.12 cm, b = 10.3 cm, and L = 33.9 cm. What is the magnitude of the net force on the loop due i_1?

Solution

Here,

i1 = 29.3 A

i2 = 21.7 A

for the net force on the loop

Fnet = F(upper) - F(low)

Fnet = u0 * i1 * i2 * L/(2pi) * (1/a - 1/(a +b))

Fnet = 4pi *10^-7 * 29.3 * 21.7 * 0.339/(2pi) * (1/(0.0112) + 1/(0.0112 + 0.103))

solving

Fnet = 4.23 *10^-3 N

the net force on the loop is 4.23 *10^-3 N