Question

Lorentz magnetic force is acting on a particle of charge q moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$. The work done by this force on the charged particle is}

• A. zero
• B. one
• C. infinity
• D. $qB \sin \theta$

Hint:

Magnetic force only changes the direction of velocity, not its magnitude (kinetic energy).

Answer 1

The Correct Option is A

Step 1: Formula
Magnetic force $\vec{F} = q(\vec{V} \times \vec{B})$.

Step 2: Analysis
By the definition of a cross product, the force $\vec{F}$ is always perpendicular to the velocity $\vec{V}$.

Step 3: Calculation
Power $P = \vec{F} \cdot \vec{V} = 0$ (since angle is $90^{\circ}$).
Since Power is the rate of doing work, and Power is 0, the Work Done is 0.

Step 4: Conclusion
Magnetic forces do no work on moving charges. Final Answer: (A)