Lenz's Law describes how the direction of an induced current (and thus the magnetic force) is such that it opposes the change in the magnetic flux that caused it. The law itself doesn't have a single "formula" for the force, but it helps determine the direction of the force.
However, the force involved in Lenz's Law can be described using the following formula for the magnetic force on a current-carrying wire:
\[
F = I \cdot L \cdot B \cdot \sin(\theta)
\]
Where:
- \( F \) is the force on the wire.
- \( I \) is the current in the wire, which is induced by the changing magnetic field (this is where Lenz's Law plays a role in determining the direction of the current).
- \( L \) is the length of the wire in the magnetic field.
- \( B \) is the magnetic field strength.
- \( \theta \) is the angle between the magnetic field \( B \) and the direction of current \( I \).
In the context of Lenz's Law, the direction of the current is such that it creates a magnetic field that opposes the change in the magnetic flux. This results in a force that opposes the motion causing the change in flux (for example, the movement of a magnet or the change in current in a nearby coil).