# Magnetic Force Between Parallel Wires Formula

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?

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?

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
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