1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other with a force of $$\mathrm{F}$$. Another identical uncharged sphere $$\mathrm{C}$$ is first placed in contact with $$\mathrm{A}$$ and then in contact with $$\mathrm{B}$$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

A
3F/2
B
3F/4
C
F
D
2F
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

A spherically symmetric charge distribution is considered with charge density varying as

$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases}$$

Where, $$r(r < R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be:

A
$$\frac{\rho_{0} \mathrm{r}}{4 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$$
B
$$\frac{\rho_{0} r}{3 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$$
C
$$\frac{\rho_{0} r}{4 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$$
D
$$\frac{\rho_{0} r}{5 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$$
3
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

Given below are two statements.

Statement I : Electric potential is constant within and at the surface of each conductor.

Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options given below.

A
Both Statement I and Statement II are correct
B
Both Statement I and Statement II are incorrect
C
Statement I is correct but Statement II is incorrect
D
Statement I is incorrect but Statement II is correct
4
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

A uniform electric field $$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$ is created between two parallel plates of length $$1 \mathrm{~m}$$ as shown in figure, (where $$\mathrm{m}=$$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The angle of the deviation $$(\theta)$$ of the path of the electron as it comes out of the field will be _________.

A
$$\tan ^{-1}(4)$$
B
$$\tan ^{-1}(2)$$
C
$$\tan ^{-1}\left(\frac{1}{3}\right)$$
D
$$\tan ^{-1}(3)$$
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