1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
A point source of $100 \mathrm{~W}$ emits light with $5 \%$ efficiency. At a distance of $5 \mathrm{~m}$ from the source, the intensity produced by the electric field component is:
A
$\frac{1}{40 \pi} \frac{W}{m^2}$
B
$\frac{1}{10 \pi} \frac{W}{m^2}$
C
$\frac{1}{20 \pi} \frac{W}{m^2}$
D
$\frac{1}{2 \pi} \frac{W}{m^2}$
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ is given by:

$(\mathrm{I}: r < a, \mathrm{II}: a < r < b$, III: $r>b$ )

A
$E_I=0, E_{I I}=0, E_{I I I} \neq 0$
B
$E_I \neq 0, E_{I I}=0, E_{III}=0$
C
$E_I \neq 0, E_{I I}=0, E_{III} \neq 0$
D
$E_I=0, E_{I I}=0, E_{I I I}=0$
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$$ are :

A
$$\mathrm{Nm}^{2} \mathrm{C} ; \mathrm{Nm}^{3} \mathrm{C}$$
B
$$\mathrm{Nm}^{3} \mathrm{C}^{-1} ; \mathrm{Nm}^{2} \mathrm{C}^{-1}$$
C
$$\mathrm{Nm}^{3} \mathrm{C} ; \mathrm{Nm}^{2} \mathrm{C}$$
D
$$\mathrm{Nm}^{2} \mathrm{C}^{-1} ; \mathrm{Nm}^{3} \mathrm{C}^{-1}$$
4
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $$\sigma^{\prime}$$. The ratio $$\frac{\sigma^{\prime}}{\sigma}$$ is :

A
$$\frac{5}{3}$$
B
$$\frac{5}{6}$$
C
$$\frac{9}{4}$$
D
$$\frac{4}{3}$$
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