Magnetic Force Between Parallel Wires Formula

For the case of a long straight wire carrying a current I₁, and a wire carrying a current I₂, the force that each wire feels due to the presence of the other depends on the distance between them and the magnitude of the currents.

For per unit length = magnetic permeability * (current 1) *(current 2) / (2 π distance between the wires)

The equation is:

F/ΔL = μ I₁ I₂ /2 π r

Where:

μ: permeability

I₁: current intensity flowing in the cable one

I₂: current intensity flowing in the cable two

r: distance between wires

Parallel wire Formula Questions:

1) Two wires separate by 10 cm carry a current I₁= 2 A and I₂= 1 A respectively. what is the force per unit length between the wires?

Answer:

From the formula of the two parallel wires we substitute the values,

F/ΔL = 4π *10^(-7) T*m/A * 2 A * 1 A/(2 π *0.1 m)

= 4*10^(-6) N/m

2) Two wires which feels a force per unit length of 20*10^(-6) N/m, carry a current I₁= 2 A and I₂= 1 A respectively. What is the distance between the wires?

Answer:

From the formula of the two parallel wires we find the distance between them,

r= μ I₁ I₂ /(2 π (F/ΔL)) = 4π *10^(-7) T*m/A * 2 A * 1 A/(2 π * 20*10^(-6)N/m)

= 0.2*10^(-1) m