Question

The electrostatic force ($\vec{F_1}$) and magnetic force ($\vec{F_2}$) acting on a charge $q$ moving with velocity $\vec{v}$ can be written:

• A. $\vec{F_1} = q \vec{V} \cdot \vec{E}, \quad \vec{F_2} = q (\vec{B} \cdot \vec{V})$
• B. $\vec{F_1} = q \vec{B}, \quad \vec{F_2} = q (\vec{B} \times \vec{V})$
• C. $\vec{F_1} = q \vec{E}, \quad \vec{F_2} = q (\vec{V} \times \vec{B})$
• D. $\vec{F_1} = q \vec{E}, \quad \vec{F_2} = q (\vec{B} \times \vec{V})$

Answer 1

Answer: (C)

$\vec{F_1} = q \vec{E}, \quad \vec{F_2} = q (\vec{V} \times \vec{B})$

Answer 2

The electrostatic force acting on a charged particle is given by:

$\vec{F}_1 = q\vec{E},$

where:
- $q$ is the charge of the particle,
- $\vec{E}$ is the electric field.

The magnetic force acting on a charged particle moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force law:

$\vec{F}_2 = q(\vec{v} \times \vec{B}),$

where:
- $q$ is the charge of the particle,
- $\vec{v}$ is the velocity of the particle,
- $\vec{B}$ is the magnetic field.

Therefore, the correct expressions for the electrostatic and magnetic forces are:

$\vec{F}_1 = q\vec{E}, \quad \vec{F}_2 = q(\vec{v} \times \vec{B}).$

Hence, the correct option is (3).