1
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :
A
F
B
$${{3F} \over 4}$$
C
$${{3F} \over 8}$$
D
$${{F} \over 2}$$
2
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over b} + a} \right]$$
3
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${{3{\rho _o}{R^3}} \over {4{ \in _o}{r^2}}}$$
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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 $$x=0.$$
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