Question

a. Two long parallel wires that are a distance 2a apart carry equal currents I into the plane of the page as shown above.

i. Determine the resultant magnetic field intensity at the point O midway between the wires.

ii. Develop an expression for the resultant magnetic field intensity at the point N. which is a vertical distance y above point O. On the diagram above indicate the direction of the resultant magnetic field at point N.

Answer 1

(a) i) The field from a wire is given by B = μ_oI / (2πR), with R and I equal for both wires at point O. Based on the RHR for the current wires, the right wire makes a field down and the left wire makes a field up so cancel to zero.

ii.

Based on the RHR, the resultant fields from each wire are directed as shown. Since the distance to each wire is the same, the resultant B field will simply be twice the x component of one of the wire’s B fields.

The distance to point N is  so the total field at that location from a single wire is

 

The x component of that field is given by B cos θ, where cos θ can be replaced with cos θ = a/h