1
JEE Main 2017 (Offline)
+4
-1
An electric dipole has a fixed dipole moment $$\overrightarrow p$$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to$$ . The angle $$\theta$$ is:
A
90o
B
45o
C
30o
D
60o
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Within a spherical charge distribution of charge density $$\rho$$(r), N equipotential surfaces of potential V0, V0 + $$\Delta$$V, V0 + 2$$\Delta$$V, .......... V0 + N$$\Delta$$V ($$\Delta$$ V > 0), are drawn and have increasing radii r0, r1, r2,..........rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and $$\Delta$$V then :
A
$$\rho$$ (r) $$\alpha$$ r
B
$$\rho$$ (r) = constant
C
$$\rho$$ (r) $$\alpha$$ $${1 \over r}$$
D
$$\rho$$ (r) $$\alpha$$ $${1 \over {{r^2}}}$$
3
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
4
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
$${Q \over {2\pi \,\left( {{b^2} - {a^2}} \right)}}$$
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