Lorentz force on a moving charge (\( q \)) can be calculated by using the following formula (where symbols have their usual meaning)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) \)
The Lorentz force on a charge q moving with velocity \( \vec{v} \) through an electric field \( \vec{E} \) and a magnetic field \( \vec{B} \) is the sum of the electric force and the magnetic force.
\( \vec{F} = q\vec{E} + q(\vec{v}\times\vec{B}) = q(\vec{E} + \vec{v}\times\vec{B}) \)
The magnetic part is a cross product: it acts perpendicular to both \( \vec{v} \) and \( \vec{B} \), so it changes the direction of motion but does no work.
NCERT (2026-27):
Magnetic Field, Lorentz Force – “Let us suppose that there is a point charge \( q \) (moving with a velocity \( \mathbf{v} \) and, located at \( \mathbf{r} \) at a given time \( t \)) in presence of both the electric field \( \mathbf{E}(\mathbf{r}) \) and the magnetic field \( \mathbf{B}(\mathbf{r}) \). The force on an electric charge \( q \) due to both of them can be written as
\( \displaystyle \mathbf{F} = q\,[\,\mathbf{E}(\mathbf{r}) + \mathbf{v}\times\mathbf{B}(\mathbf{r})\,] \equiv \mathbf{F}_{\mathrm{electric}} + \mathbf{F}_{\mathrm{magnetic}} \qquad (4.3) \)
This force was given first by H.A. Lorentz based on the extensive experiments of Ampere and others. It is called the Lorentz force.”