লরেঞ্জ বলের সংজ্ঞা

The Lorentz force is the force exerted by a magnetic field on a charged moving particle. As mentioned in a previous article (Motion of a Charge in a Uniform Magnetic Field), a moving charged particle will be pulled in a direction that is perpendicular to its current velocity. This is caused by the Lorentz force. This force can be calculated using the following equation: $$\vec{F} = q \vec{v}\times \vec{B}$$

This means that the magnitude of the force is: $$|\vec{F}| = q |\vec{v}| |\vec{B}|\sin{\theta}$$ where $\theta$ equals the angle between $\vec{v}$ and $\vec{B}$

The derivation of this formula involves complex calculus starting from the Biot-Savart Law, which is too lengthy and complicated to explain here.

However, there are certain interesting implications of the above formula, for example, we can derive the force experienced by a current carrying wire within a magnetic field. Note that the total force experienced by the wire is equal to the sum of all forces experienced by individual charges within the wire. Each charge has equal $q$ and their $\vec{v}$ is the drifting velocity within the wire. We know that current is equal to drift velocity times charge divided by the length. We get: $$\vec{F} = \frac{q\vec{V}}{L}L\times\vec{B}$$ $$\vec{F} = L\vec{I}\times\vec{B}$$