Acurrent-carrying wire is bent into a circular loop of radius r and lies in an xy plane. a uniform external magnetic field b in the +z direction exists throughout the plane of the loop. the current has the magnitude of i and it is deirected counterclockwise when observing from positive z axis. what is the magnetic force exerted by the external field on the loop?
express your answer in terms of some or all of the variables i, r, and b

 F = 2π I R B

Explanation:

The magnetic force is described by the equation.

      F = q v x B = i L  x B

Where i is the current, L is a vector that points in the direction of the current (length) and B is the magnetic field.

This equation can be used in scalar form and the direction of the force found by the right hand ruler, the thumb goes in the direction of L, the fingers extended in the direction of B and the palm of the hand indicates the direction of the force if the load is positive

     F = i L B sin θ

In this case the wire is in the xy plane and the z-axis field whereby they are perpendicular, θ = 90º and sin 90 = 1

     F = i L B

The loop length is

    L = 2π R

    F = i 2π R B

    F = 2π I R B

The force is in the loop