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1
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
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.
A
0.424 nC m$$-$$2
B
4.0 nC m$$-$$2
C
47.88 C/m
D
0.07 nC m$$-$$2
2
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Given below are two statements:

Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..

In the light of the above statements, choose the correct answer from the options given below :
A
Both Statement I and Statement II are true
B
Statement I is false but Statement II is true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false
3
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

[g = 9.8 m/s2; $$\sin 30^\circ = {1 \over 2}$$; $$\cos 30^\circ = {{\sqrt 3 } \over 2}$$] A
0.46 s
B
0.92 s
C
1.3 s
D
2.3 s
4
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$. A
$${Q \over {4\pi {\varepsilon _0}{L^2}}}$$
B
$${Q \over {3\pi {\varepsilon _0}{L^2}}}$$
C
$${Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}$$
D
$${{\sqrt 3 Q} \over {4\pi {\varepsilon _0}{L^2}}}$$
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