CBSE Class 12 Physics 2023: question 23(a)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Lorentz (magnetic) force: $\vec{F}=q(\vec{v}\times \vec{B})$, whose magnitude is $F=qvB\sin \theta$.

   ½ mark

2. The force is maximum, $F_{max}=qvB$, when $\theta =90^{\circ }$, i.e. when $\vec{v}\perp \vec{B}$.

   ½ mark

3. Work done: $\vec{F}$ is always perpendicular to $\vec{v}$, and hence to the displacement $d\vec{r}=\vec{v}dt$. So $W={\int }_{{\vec{r}}_1}^{{\vec{r}}_2}\vec{F}\cdot d\vec{r}=\int q(\vec{v}\times \vec{B})\cdot \vec{v}dt=0$, because $(\vec{v}\times \vec{B})\cdot \vec{v}=0$. Each element of work is $Fdr\cos 90^{\circ }=0$, so no work is done and the speed (kinetic energy) of the particle remains constant.

   1 mark

Answer: $\vec{F}=q(\vec{v}\times \vec{B})$; maximum when $\vec{v}\perp \vec{B}$; W = 0 since $\vec{F}\perp d\vec{r}$

Revise the chapter

• Chapter: Moving Charges and Magnetism (notes, formulas, where marks are lost and every past question)