Question

A charge \( q \) moves with velocity \( \vec{v} \) through electric field \( \vec{E} \) as well as magnetic field \( \vec{B} \). Then the force acting on it is

• A. \( q(\vec{v} \times \vec{B}) \)
• B. \( q\vec{E} + q(\vec{v} \times \vec{B}) \)
• C. \( q(\vec{E} \times \vec{v}) \)
• D. \( q (\vec{B} \times \vec{v}) \)

Hint:

The Lorentz force equation gives the total force acting on a charged particle in the presence of both electric and magnetic fields.

Answer 1

The Correct Option is B

Step 1: Lorentz force.
The force acting on a charge moving through electric and magnetic fields is given by the Lorentz force law: \[ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) \] This equation gives the total force acting on the particle due to both electric and magnetic fields.
Step 2: Conclusion.
Thus, the correct answer is (B) \( q\vec{E} + q(\vec{v} \times \vec{B}) \).