What is the magnetic force per unit length between two parallel wires, separated by a distance `d` , each carrying a current `I ` in the same direction?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The magnetic field produced by a current carrying wire is:

`B=(mu_0 I)/(2pi r)=(mu_0 I)/(2pi d)`

Then use the lorentz force law per unit length is

`F/L=q/L(v xx B)=lambda (v xx B)=(lambda*v xx B)=I xx B=I*(mu_0 I)/(2pi d) `

`F/L=(mu_0 I^2)/(2pi d)`

Now lets find the direction of the force. I...

View
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The magnetic field produced by a current carrying wire is:

`B=(mu_0 I)/(2pi r)=(mu_0 I)/(2pi d)`

Then use the lorentz force law per unit length is

`F/L=q/L(v xx B)=lambda (v xx B)=(lambda*v xx B)=I xx B=I*(mu_0 I)/(2pi d) `

`F/L=(mu_0 I^2)/(2pi d)`

Now lets find the direction of the force. I will use cylindrical coordinates `(r,phi,z)` . Let the current go in the `z ` direction. Then the magnetic field will wrap around the wire in the `phi` direction by the right hand rule. Now lets look at the cross product.

`F=I xx B=z xx phi=-r`

Therefore, the magnetic force on the other wire is directed radially inward or toward the wire. You would find the same answer for the other wire. Hence the magnetic force is attractive for wires with currents in the same direction.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
Approved by eNotes Editorial Team