If a charged particle at rest experiences no electromagnetic force, then which of the following statements are true?
A. the electric field must be zero
B. the magnetic field must be zero
C. the electric field may or may not be zero
D. the magnetic field may or may not be zero
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A and D only
The electromagnetic (Lorentz) force on a charge is
\( \displaystyle \vec{F} = q\vec{E} + q\,\vec{v}\times\vec{B} \)
For a particle at rest, \( \vec{v} = 0 \), so the magnetic force is zero whatever B is, and the total force reduces to \( q\vec{E} \). No force therefore means \( \vec{E} = 0 \).
(A) the electric field must be zero — Correct. The only possible force is \( q\vec{E} \), and it is zero only if \( \vec{E} = 0 \).
(B) the magnetic field must be zero — Incorrect. A magnetic field exerts no force on a stationary charge, so B need not be zero.
(C) the electric field may or may not be zero — Incorrect. A non-zero E would push the charge, so E must be zero.
(D) the magnetic field may or may not be zero — Correct. B has no effect on a charge at rest, so nothing can be concluded about it.
NCERT (2026-27):
Magnetic Field, Lorentz Force – “… The force on an electric charge q due to both of them can be written as
\( \displaystyle \mathbf{F} = q\left[\mathbf{E}(\mathbf{r}) + \mathbf{v} \times \mathbf{B}(\mathbf{r})\right] \equiv \mathbf{F}_{\text{electric}} + \mathbf{F}_{\text{magnetic}} \qquad (4.3) \)”
Magnetic Field, Lorentz Force – “… It is called the Lorentz force.”
Magnetic Field, Lorentz Force – “… (iii) The magnetic force is zero if charge is not moving (as then |v| = 0). Only a moving charge feels the magnetic force.”