Question

Derive an expression for magnetic force. How is the direction of magnetic force determined?

Hint:

Use the right-hand rule to determine the direction of the magnetic force on a moving charge in a magnetic field: curl your fingers in the direction of the magnetic field and the force will be along your thumb for positive charges.

Answer 1

Step 1: Expression for magnetic force.
The magnetic force \( \vec{F} \) on a moving charge \( q \) with velocity \( \vec{v} \) in a magnetic field \( \vec{B} \) is given by the Lorentz force law: \[ \vec{F} = q (\vec{v} \times \vec{B}) \] This is a vector equation, where the force is perpendicular to both the velocity of the charge and the magnetic field.
Step 2: Direction of the magnetic force.
The direction of the magnetic force is given by the right-hand rule. Point your fingers in the direction of the velocity of the charged particle, curl them in the direction of the magnetic field, and your thumb will point in the direction of the force acting on a positive charge. For a negative charge, the force direction will be opposite.
Step 3: Conclusion.
Thus, the magnetic force on a charged particle moving in a magnetic field is given by \( \vec{F} = q (\vec{v} \times \vec{B}) \), and its direction can be determined using the right-hand rule.