Question

A charge moves with velocity 'V' through electric field (E) as well as magnetic field (B). then the force acting on it is

• A. $q (\vec{B} \times \vec{V})$
• B. . then the force acting on it is
• C. $q \vec{E} + q (\vec{V} \times \vec{B})$
• D. $q (\vec{E} \times \vec{V})$

Hint:

The Lorentz force is a fundamental principle in electromagnetism. Remember that the electric force acts in the direction of the field (for positive charges), while the magnetic force is perpendicular to both the velocity vector and the magnetic field vector.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the total force (Lorentz force) acting on a charged particle moving through a region containing both electric and magnetic fields.

Step 2: Key Formula or Approach:
The total force is the vector sum of the electric force and the magnetic (Lorentz) force.

Step 3: Detailed Explanation:
1. The force due to an electric field $\vec{E}$ on a charge $q$ is given by $\vec{F}_e = q \vec{E}$.
2. The force due to a magnetic field $\vec{B}$ on a charge $q$ moving with velocity $\vec{V}$ is given by $\vec{F}_m = q (\vec{V} \times \vec{B})$.
3. The total force $\vec{F}$ is the sum of these two forces: $\vec{F} = \vec{F}_e + \vec{F}_m = q \vec{E} + q (\vec{V} \times \vec{B})$.

Step 4: Final Answer:
The total force is $q \vec{E} + q (\vec{V} \times \vec{B})$, which corresponds to option (C).