1
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
The potential (in volts) of a charge distribution is given by.

V(z) = 30 $$-$$ 5x2 for $$\left| z \right|$$ $$\le$$ 1 m.
V(z) = 35 $$-$$ 10 $$\left| z \right|$$ for $$\left| z \right|$$ $$\ge$$1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $${\rho _0}$$ (in units of $${\varepsilon _0}$$) which is spread over a certain region, then choose the correct statement.
A
$${\rho _0}$$ = 10 $${\varepsilon _0}$$ for $$\left| z \right|$$ $$\le$$ 1 m and $${\rho _0} = 0$$ elsewhere
B
$${\rho _0}$$ = 20 $${\varepsilon _0}$$ in the entire region
C
$${\rho _0}$$ = 40 $${\varepsilon _0}$$ in the entire region
D
$${\rho _0}$$ = 20 $${\varepsilon _0}$$ for $$\left| z \right|$$ $$\le$$ 1 m and $${\rho _0} = 0$$ elsewhere
2
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
$${Q \over {2\pi \,\left( {{b^2} - {a^2}} \right)}}$$
3
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
4
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
$$80$$ $$J/C$$
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