1
JEE Main 2018 (Offline)
+4
-1
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$+ \sigma$$, $$- \sigma$$ and $$+ \sigma$$ respectively. The potential of shell B is :
A
$${\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over c} + a} \right]$$
B
$${\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over a} + c} \right]$$
C
$${\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over b} + c} \right]$$
D
$${\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over b} + a} \right]$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
A solid ball of radius R has a charge density $$\rho$$
given by $$\rho$$ = $$\rho$$o (1 $$-$$ $${\raise0.5ex\hbox{\scriptstyle r} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle R}}$$) for 0 $$\le$$ r $$\le$$ R. The electric field outside the ball is :
A
$${{{\rho _o}{R^3}} \over {{ \in _o}{r^2}}}$$
B
$${{{\rho _o}{R^3}} \over {12{ \in _o}{r^2}}}$$
C
$${{4{\rho _o}{R^3}} \over {3{ \in _o}{r^2}}}$$
D
$${{3{\rho _o}{R^3}} \over {4{ \in _o}{r^2}}}$$
3
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 $$x=0.$$
4
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
$${Q \over {6{ \in _0}}}$$
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