1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium position, taken to be at $$x=0,$$ with an amplitude $$A$$. An electric field $$E$$ is applied along the $$x$$-direction. Which of the following statements is correct ?
A
The new equilibrium position is at a distance $${{qE} \over {2k}}$$ from $$x=0.$$
B
The total energy of the system is $${1 \over 2}m{\omega ^2}{A^2} + {1 \over 2}{{{q^2}{E^2}} \over k}.$$
C
The total energy of the system is $${1 \over 2}m{\omega ^2}{A^2} - {1 \over 2}{{{q^2}{E^2}} \over k}.$$
D
The new equilibrium position is at a distance $${{2qE} \over k}$$ from $$x=0.$$
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.

The electric flux through the square surface is
A
$${Q \over {{ \in _0}}}$$
B
$${Q \over {2{ \in _0}}}$$
C
$${Q \over {3{ \in _0}}}$$
D
$${Q \over {6{ \in _0}}}$$
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surfaces be $${\Phi _1},$$ $${\Phi _2},$$ $${\Phi _3}$$ and $${\Phi _4}$$. Then :
A
$${\Phi _1}$$ < $${\Phi _2}$$ = $${\Phi _3}$$ > $${\Phi _4}$$
B
$${\Phi _1}$$ > $${\Phi _2}$$ > $${\Phi _3}$$ > $${\Phi _4}$$
C
$${\Phi _1}$$ = $${\Phi _2}$$ = $${\Phi _3}$$ = $${\Phi _4}$$
D
$${\Phi _1}$$ > $${\Phi _3}$$ ; $${\Phi _2}$$ < $${\Phi _4}$$
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field ?
A
589.5 V
B
589.2 V
C
589.4 V
D
589.6 V
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