1
JEE Main 2016 (Offline)
+4
-1
The region between two concentric spheres of radii $$'a'$$ and $$'b',$$ respectively (see figure), have volume charge density $$\rho = {A \over r},$$ where $$A$$ is a constant and $$r$$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :

A
$${{2Q} \over {\pi \left( {{a^2} - {b^2}} \right)}}$$
B
$${{2Q} \over {\pi \,{a^2}}}$$
C
$${Q \over {2\pi \,{a^2}}}$$
D
$${Q \over {2\pi \,\left( {{b^2} - {a^2}} \right)}}$$
2
JEE Main 2015 (Offline)
+4
-1
A long cylindrical shell carries positives surfaces change $$\sigma$$ in the upper half and negative surface charge - $$\sigma$$ in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures are schematic and not drawn to scale)
A
B
C
D
3
JEE Main 2014 (Offline)
+4
-1
Assume that an electric field $$\overrightarrow E = 30{x^2}\widehat i$$ exists in space. Then the potential difference $${V_A} - {V_O},$$ where $${V_O}$$ is the potential at the origin and $${V_A}$$ the potential at $$x=2$$ $$m$$ is :
A
$$120$$ $$J/C$$
B
$$-120$$ $$J/C$$
C
$$-80$$ $$J/C$$
D
$$80$$ $$J/C$$
4
JEE Main 2013 (Offline)
+4
-1
Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and charge $${q_0} = {q \over 2}$$ is placed at the origin. If charge $${q_0}$$ is given a small displacement $$\left( {y < < a} \right)$$ along the $$y$$-axis, the net force acting on the particle is proportional to
A
$$y$$
B
$$-y$$
C
$${1 \over y}$$
D
$$-{1 \over y}$$
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