1
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho$$(r) = kr, where r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite points, at equal distance, $$a$$ from the centre. If A and B do not experience any force, then :
A
$$a = {8^{ - 1/4}}R$$
B
$$a = {2^{ - 1/4}}R$$
C
$$a = {{3R} \over {{2^{1/4}}}}$$
D
$$a = {R \over {\sqrt 3 }}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $$\overrightarrow P$$ as shown. In this case :
A
surface charge density on the inner surface is uniform and equal to $${{\left( {Q/2} \right)} \over {4\pi {a^2}}}$$
B
surface charge density on the inner surface of the shell is zero everywhere
C
surface charge density on the outer surface depends on $$\left| {\overrightarrow P } \right|$$
D
electric field outside the shell is the same as that of a point charge at the centre of the shell
3
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A point dipole $$\overrightarrow p = - {p_0}\widehat x$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)
A
$${{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}$$
B
$$0,{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}$$
C
$${{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}$$
D
$$0,{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}$$
4
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
In free space, a particle A of charge 1$$\mu$$C is held fixed at a point P. Another particle B of the same charge and mass 4$$\mu$$g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : $$\left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]$$
A
1.0 m/s
B
6.32 $$\times$$ 104 m/s
C
2.0 $$\times$$ 103 m/s
D
1.5 $$\times$$ 102 m/s
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