1
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

A cubical volume is bounded by the surfaces $$\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}$$. The electric field in the region is given by $$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}$$. Where $$\mathrm{E}_{0}=4 \times 10^{4} ~\mathrm{NC}^{-1} \mathrm{~m}^{-1}$$. If $$\mathrm{a}=2 \mathrm{~cm}$$, the charge contained in the cubical volume is $$\mathrm{Q} \times 10^{-14} \mathrm{C}$$. The value of $$\mathrm{Q}$$ is ________________.

(Take $$\epsilon_{0}=9 \times 10^{-12} ~\mathrm{C}^{2} / \mathrm{Nm}^{2}$$)

2
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$\mathrm{q}_{0}$$ becomes maximum is $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is __________.

3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$$. The electric flux through the cube of side $$20 \mathrm{~cm}$$ when placed in electric field (as shown in the figure) is __________ $$\mathrm{V} \mathrm{~cm}$$.

4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
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 $1 \times 2 \times 3 \mathrm{~m}^{3}$ )