QJEEM23Ph9236: JEE Main 2023 Physics - Class 12 JEEM23Ph9236 Solution: As shown in figure, a cuboid lies in a region with electric…

Question

Verified Solution • 2025–26 Session moderate

As shown in figure, a cuboid lies in a region with electric field

E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} / \mathrm{C}

. The magnitude of charge within the cuboid is

n \in_{0} C

.

The value of

n

is _________ (if dimension of cuboid is

1 \times 2 \times 3 \mathrm{~m}^{3}

)

Accepted Answer

Flux through planes parallel to

y-z=2(1)^{2} \times

Area

\begin{aligned}&amp; =2(1)^{2} \times 2 \times 3 \\\\&amp; =12 \mathrm{Nm}^{2} / \mathrm{C}\end{aligned}

Flux through planes parallel to

x-z=-4(2) \times

Area

\begin{aligned}&amp; =-4(2) \times 1 \times 3 \\\\&amp; =-24 \mathrm{Nm}^{2} / \mathrm{C}\end{aligned}

Flux through planes parallel to

x-y=0

\Rightarrow \phi

Total

=12-24=-12

\Rightarrow-12=\frac{q_{\mathrm{enc}}}{\varepsilon_{0}} \Rightarrow\left|q_{\mathrm{enc}}\right|=12 \varepsilon_{0}

\Rightarrow n=12

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