2. Magnetic Force on a Moving Charge

Concept Explanation:
When a charged particle moves through a magnetic field, it experiences a force known as the Lorentz force. This force acts perpendicular to both the velocity of the particle and the magnetic field, causing the particle to move in a circular or helical path.

Formula:
The magnitude of the Lorentz force F is given by:
F = q × v × B × sin(θ)
where:
q is the charge of the particle,
v is the velocity of the particle,
B is the magnetic field strength,
θ is the angle between the velocity vector and the magnetic field.

Right-Hand Rule for Lorentz Force:
Similar to the current-carrying conductor, the right-hand rule can be used to determine the direction of the force. Point your thumb in the direction of the velocity of the positive charge, your fingers in the direction of the magnetic field, and the force is directed out of your palm.

Example Problem:
A proton with charge 1.6 × 10^-19 C is moving with a speed of 2 × 10^6 m/s in a magnetic field of 0.1 T at an angle of 90° to the field. Calculate the force acting on the proton.

Solution:
Using the formula:
F = q × v × B × sin(θ)
F = 1.6 × 10^-19 × 2 × 10^6 × 0.1 × sin(90°)
F = 3.2 × 10^-14 N
So, the force acting on the proton is 3.2 × 10^-14 N.