# A particle of mass $m$ and charge q is in an electric and magnetic field given by

Question:

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by

$\overrightarrow{\mathrm{E}}=2 \hat{i}+3 \hat{j} ; \overrightarrow{\mathrm{B}}=4 \hat{j}+6 \hat{k}$

The charged particle is shifted from the origin to the point $\mathrm{P}(x=1 ; y=1)$ along a straight path. The magnitude of the total work done is :

1. (1) $(0.35) \mathrm{q}$

2. (2) $5 \mathrm{q}$

3. (3) (2.5)q

4. (4) $(0.15) \mathrm{q}$

Correct Option: , 2

Solution:

(2) Resultant force on the charged particle

$=\overrightarrow{\mathrm{F}}_{\text {net }}=\mathrm{q} \overrightarrow{\mathrm{E}}+\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})$

$=(2 q \hat{i}+3 q \hat{j})+q(\vec{v} \times \vec{B})$

Also $\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})=0$

So, required work done\

$\mathrm{W}=\overrightarrow{\mathrm{F}}_{\text {net }} \overrightarrow{\mathrm{S}}=(2 \mathrm{q} \hat{\mathrm{i}}+3 \hat{\mathrm{q}}) \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}})$

$=2 q+3 q$

$=5 q$