Question

A small current-carrying loop is located at a distance r from a long straight conductor with current I. The magnetic moment of the loop is equal to P_m. Find the magnitude and direction of the force vector applied to the loop if the vector P_m 

(a) is parallel to the straight conductor; 

(b) is oriented along the radius vector r; 

(c) coincides in direction with the magnetic field produced by the current I at the point where the loop is located.

Answer 1

Due to the straight conductor, 

We use the formula, 

(a) The vector P_m is parallel to the straight conductor. 

because neither the direction nor the magnitude of depends on z

(b) The vector  P_m is oriented along the radius vector r

The direction of at r + dr is parallel to the direction at r. Thus only the φ component of  vector F will survive. 

(c) The vector P_m coincides in direction with the magnetic field, produced by the conductor carrying current I