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. $q (\vec{V} \times \vec{B})$
• 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: Picture the setup.
A charge $q$ is moving with velocity $\vec{V}$ in a region where both an electric field $\vec{E}$ and a magnetic field $\vec{B}$ are present. We want the total force on it.

Step 2: Two pushes act at once.
The charge feels two separate forces, one from the electric field and one from the magnetic field, and we simply add them.

Step 3: The electric part.
An electric field pushes a charge whether it moves or not. That force is $\vec{F}_e = q\vec{E}$, pointing along the field.

Step 4: The magnetic part.
A magnetic field only pushes a charge that is moving, and the force is sideways to both the velocity and the field. That force is $\vec{F}_m = q(\vec{V} \times \vec{B})$.

Step 5: Add them as vectors.
The total (Lorentz) force is $\vec{F} = \vec{F}_e + \vec{F}_m = q\vec{E} + q(\vec{V} \times \vec{B})$.

Step 6: Pick the matching option.
This complete expression is option (C).
\[ \boxed{\vec{F} = q\vec{E} + q(\vec{V} \times \vec{B})} \]