The diagram shows a long, straight wire that carries a steady current I. Two wir
ID: 2076090 • Letter: T
Question
The diagram shows a long, straight wire that carries a steady current I. Two wire loops lie in the plane of the wire. The center of each loop is at a distance r from the center of the wire. The square loop has side length 'a' and the circular loop has diameter 'a'. Each loop carries a current I that flows in the 'clockwise' direction. The loops are very far apart, such that you can neglect any interaction between them. a) Does each loop experience a net attractive or a net repulsive force? b) Calculate the net force on the square loop in terms of l, r, and a. c) Evaluate your expression for value of 'r' much greater than 'a' and express the result in terms of the magnetic moment of the square loop. d) Using energy considerations, find the net force acting on the circular loop for the condition that r > > a. Is it larger or smaller than the result of c)? Explain why this is so.Explanation / Answer
a) attractive force because left side will experience larger attractive force amd right side will experience smaller repulsive force as left side is nearer to the wire.
B) Fnet = (i*a*uo i/2pi) (1/(r-0.5a)) - 1/(r+0.5a))
= (uoi^2 a / 2pi)*(a/(r^2 - 0.25a^2))
C) Fnet = (uoi^2/ 2pi)*(a^2/r^2 )
D) Replacing area of square with circle
Fnet = (uoi^2/ 2pi)*(0.25pi a^2/r^2 )
= (uoi^2/8)*(a^2/r^2 )
It is smaller because area is smaller