An electric field, overrightarrow{mathrm{E}}=frac{2 hat{mathrm{i}}+6 hat{mathrm{j}}+8 hat{mathrm{k}}

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1. Electric Charges and Fields

hard

An electric field, $\overrightarrow{\mathrm{E}}=\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}$ passes through the surface of $4 \mathrm{~m}^2$ area having unit vector $\hat{\mathrm{n}}=\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)$. The electric flux for that surface is $\mathrm{Vm}$

$12$

$13$

$15$

$16$

(JEE MAIN-2024)

Solution

$\phi =\overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{A}}$

$=\left(\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}\right) \cdot 4\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)$

$=\frac{4}{6} \times(4+6+8)=12 \mathrm{Vm}$

Standard 12

Physics

Find out the surface charge density at the intersection of point $x =3\, m$ plane and $x$ -axis, in the region of uniform line charge of $8\, nC / m$ lying along the $z$ -axis in free space.

hard

(JEE MAIN-2021)

As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C$. The magnitude of charge within the cuboid is $n \varepsilon_0 C$. The value of $n$ is $…………$ (if dimension of cuboid is $1 \times 2 \times 3 \;m ^3$ )

medium

(JEE MAIN-2023)

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medium

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

easy

What is the net flux of the uniform electric field of $E =3 \times 10^{3} i\; N / C $ through a cube of side $20\; cm$ oriented so that its faces are parallel to the coordinate planes?