Figure 1: A Current Loop in a Magnetic Field

For a magnetic field (vector) acting on an arm of a current loop, a square current loop and a Bohr orbit are similar. The force on each single charge (q) travelling in the arm comes from the Lorentz force:

Since is perpendicular to (in our case), the cross product simplifies. The current is given by:

where is the cross sectional area of the wire-loop, and the force on each charge is:

Since the number of charges is , the force on one arm of the loop (of length `a') is

which is reversed on the other (opposite arm) leg of the loop.

The loop is in area (and 2 a + 2 b in circumference), the moment arm about the pivot point is if is the angle between the loop and the field.

In the Figure 1, the length of the horizontal arms are `a' while the moment arm is of length `b/2', i.e., from the axis to a horizontal arm is b/2 (cm). The torque ( ) is

but, since a b is the area (A) of the loop, we have

Commonly, this torque is related to a magnetic moment equivalent, i.e.,

in analogy with an electric dipole in an electric field. A current loop is equivalent to a magnetic moment, a tiny bar magnet.

We assume that the above would hold for a Bohr orbit.

From Bohr Theory we had (for the radius):
Expression for radius, in terms of `n',`hbar',`Z',`m', and `e'

Query, is the above formula correct?