# Magnetic Force Between Parallel Wires Formula

For the case of a long straight wire carrying a current I_{1}, and a wire carrying a current I_{2}, 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 I_{1} I_{2} /2 π r

Where:

μ: permeability

I_{1}: current intensity flowing in the cable one

I_{2}: 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 I_{1}= 2 A and I_{2}= 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 I_{1}= 2 A and I_{2}= 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 I_{1} I_{2} /(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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