1
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are :

A
$${E_1} = \sigma /{\varepsilon _0},\,{E_2} = \sigma /2{\varepsilon _0}$$
B
$${E_1} = 2\sigma /{\varepsilon _0},\,{E_2} = \sigma /{\varepsilon _0}$$
C
$${E_1} = {E_2} = \sigma /2{\varepsilon _0}$$
D
$${E_1} = {E_2} = \sigma /{\varepsilon _0}$$
2
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10$$-$$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms$$-$$2]

A
12 cm
B
10 cm
C
8 cm
D
5 cm
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A
$${{\rho q{R^2}} \over {4{\varepsilon _0}}}$$
B
$${{\rho q{R^2}} \over {2{\varepsilon _0}}}$$
C
$${{q\rho } \over {4{\varepsilon _0}{R^2}}}$$
D
$${{4{\varepsilon _0}{R^2}} \over {q\rho }}$$
4
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

A vertical electric field of magnitude 4.9 $$\times$$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :

(Given : g = 9.8 m/s2)

A
1.6 $$\times$$ 10$$-$$9 C
B
2.0 $$\times$$ 10$$-$$9 C
C
3.2 $$\times$$ 10$$-$$9 C
D
0.5 $$\times$$ 10$$-$$9 C
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