Case: Read the passage and answer the question.
The force on a charge q moving with velocity \( \vec{v} \) in an electric field \( \vec{E} \) and a magnetic field \( \vec{B} \) is given by
\( \vec{F}=q(\vec{E}+\vec{v}\times\vec{B}) \)
A bar magnet is moved with a velocity v past a stationary charge q. Which of the following is true?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The magnet exerts a force on the charge q.
In \( \vec{F}=q(\vec{E}+\vec{v}\times\vec{B}) \), the charge is at rest, so \( \vec{v}=0 \) and the magnetic term \( q\vec{v}\times\vec{B} \) is zero. Any force must then come from the electric field term \( q\vec{E} \). As the magnet moves past the charge, the magnetic field at the charge changes with time. A time-varying magnetic field generates an electric field, and this induced electric field acts on the charge.
Option (1) The magnet exerts a force on the charge q. — Correct. The moving magnet sets up an induced electric field \( \vec{E} \) at the position of the charge. So the force on it is \( \vec{F}=q\vec{E} \), and this force is not zero even though the charge is at rest.
Option (2) The magnetic field lines terminate at the charge. — Incorrect. Magnetic field lines form continuous closed loops. They do not begin or end on a charge, as electric field lines do.
Option (3) The magnet does not exert any force on the charge. — Incorrect. With \( \vec{v}=0 \) only the magnetic term \( q\vec{v}\times\vec{B} \) becomes zero. This option would hold for a magnet at rest. A moving magnet changes the field at the charge, and the electric field it induces exerts the force \( q\vec{E} \).
Option (4) Magnetic monopoles exist. — Incorrect. Isolated north or south poles (magnetic monopoles) do not exist. A bar magnet always has both poles, and the force on the charge does not need a monopole.
NCERT (2026-27):
Motional Electromotive Force – “… In the case of a stationary conductor, the force on its charges is given by
\( \vec{F}=q(\vec{E}+\vec{v}\times\vec{B})=q\vec{E} \qquad (6.6) \)
since v = 0. Thus, any force on the charge must arise from the electric field term E alone. Therefore, to explain the existence of induced emf or induced current, we must assume that a time-varying magnetic field generates an electric field. … Conversely, a bar magnet in motion (or more generally, a changing magnetic field) can exert a force on the stationary charge.”