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

The Correct Option is C

The electrostatic force (\( \vec{F}_1 \)) on a charged particle is \( \vec{F}_1 = q\vec{E} \), where \( q \) is the particle's charge and \( \vec{E} \) is the electric field. The magnetic force (\( \vec{F}_2 \)) on a charged particle with velocity \( \vec{v} \) in a magnetic field \( \vec{B} \) is described by the Lorentz force law as \( \vec{F}_2 = q(\vec{v} \times \vec{B}) \), with \( q \) being the particle's charge, \( \vec{v} \) its velocity, and \( \vec{B} \) the magnetic field. Consequently, the valid formulas for the electrostatic and magnetic forces are \( \vec{F}_1 = q\vec{E} \) and \( \vec{F}_2 = q(\vec{v} \times \vec{B}) \) respectively.Thus, option (3) is correct.