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: Think of the two separate pushes.
A charge in combined fields feels an electric push and a magnetic push, and the total is their sum. This total is the Lorentz force.

Step 2: The electric part.
The electric field gives a force $q\vec{E}$, pointing along the field for a positive charge.

Step 3: The magnetic part.
The magnetic field gives a force $q(\vec{V}\times\vec{B})$, which depends on how the charge moves across the field.

Step 4: Add them.
\[ \boxed{\vec{F} = q\vec{E} + q(\vec{V}\times\vec{B})} \]