Physics - Magnetism Question with Solution | TestHub

$\text{Power P}=\frac{\text{W}}{\text{Δ}\text{t}}$

Force on conductor
$\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{b})$

$\overrightarrow{F}=-10\left(3{\widehat{a}}_z\right)\times \left(3\times {10}^{-4}{e}^{-0.2x}{\widehat{a}}_y\right)$

$\Rightarrow \overrightarrow{\mathrm{F}}=90\times {10}^{-4}\left({\mathrm{e}}^{-0.2\mathrm{x}}\right)$along with x-axis

work done on the conductor in moving along x-axis.

$\mathrm{W}=\underset{\mathrm{x}=0}{\overset{2}{\int }}\overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{d}\mathrm{x}}$

$\text{W}=\underset{0}{\overset{2}{\int }}\text{Bi}\ell \text{dx}=\underset{0}{\overset{2}{\int }}3\times {\text{10}}^{-4}{\text{e}}^{-\text{0.2x}}\times 3\times \text{10dx}$$=90\times {10}^{-4}{\left[\frac{e^{-0.2x}}{-0.2}\right]}_0^2$

$=\text{450}\times {\text{10}}^{-4}[1-{\text{e}}^{-\text{0.4}}]=\text{180}\times {\text{10}}^{-4}\mathrm{(}\text{Using}{\text{e}}^{-\text{x}}=1-\text{x}\mathrm{)}$

$\text{P}=\frac{\text{W}}{\text{Δ}\text{t}}=\frac{\text{180}\times {\text{10}}^{-4}}{5\times {\text{10}}^{-3}}=\text{3.6 W.}$

Hence, closest option is 2.97 W.
(if we used exact value of exponential term will get exact answer).