Question

Wires 1, 2, and 3 each have current moving through them to the right. I1 = 10 A, I2 = 5 A, and I3 = 8 A. Wire 2 is 15 cm long and 5 cm below wire 1. Wire 3 is 17 cm below wire 1. What is the force on wire 2?

Answer 1

F_2 = 20 x 10⁻⁶ N

Step-by-step explanation:

given,

current in right direction

I₁ = 10 A

I₂ = 5 A

I₃ = 8 A

Length of Wire 2 = 15 cm

distance between wire 1 and wire 2, r₁ = 5 cm

distance between wire 2 and 3 = r₂ = 17 - 5 = 12 cm

Force on wire 2 due to current in wire 1 and wire 2

`F_2 = B_1I_2L_2 - B_3I_2L_2`

`F_2 =(B_1 - B_3)I_2L_2`

`F_2 =(\mu_0)/(4\pi)((2I_1)/(r_1) -(2I_3)/(r_3) )I_2L_2`

μ₀ =absolute permeability of free space= 4π x 10⁻⁷ H/m

`F_2 =(4\pi * 10^(-7))/(4\pi)((2* 10)/(0.05) -(2* 8)/(0.12))* 5* 0.15`

F_2 = 20 x 10⁻⁶ N