How to calculate the magnetic force between an straight wire and a square loop?
Answers
The force between two perpendicular current carrying wires is zero. Only the sides of the square parallel to the inifinite wire contribute to the force. The force on current carrying wire in a magnetic field is F = (length of wire)*IxB = (lenght of wire)*I*B*sin(theta). If the wire is perpendicular to the magnetic field (meaning parllel to the wire creating the mag. field) then theta = pi/2 and the force becomes (length)*I*B. Anyways, you gotta find the magntic field due to the infinte wire using the law of Biot and Savart (I think the answer is someting proportional to the inverse of two times the distance fromt the wire). It is probably given in your book. Once you know the mag. field due to the inf wire as a function of distance from the wire you use the formula given in the first paragraph for parallel wires to get F= -a*I*B(d-a/2) + a*I*B(d+a/2) as the total force acting on the two parallel sides of the square. The net force should be negative (meaning directed to the left and in the plane containing the square and inf. line). You could calculate the magnetic field due to the square then find the force on the infinite wire from that magnetic field, but I don't recommed it. By the way, the side of the square closest to the wire is attracted, the side furthest is repelled (currents in the same direction attract, opposite directions repel. Oh, and here is the mag field for an infintely long wire: B= u*I/(2*Pi*a) where 'a' is the distance from the wire and 'u' is a constant.
Reference https://www.physicsforums.com/threads/force-current-between-an-infinitely-long-wire-and-a-square-loop.116190/