1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -
A
$${{Q\left( {{a^2} + {b^2} + {c^2}} \right)} \over {4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}$$
B
$${Q \over {4\pi {\varepsilon _0}\left( {a + b + c} \right)}}$$
C
$${Q \over {12\pi {\varepsilon _0}}}{{ab + bc + ca} \over {abc}}$$
D
$${{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d _B} = - 2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

A
$${{\sqrt 2 R} \over {\sqrt 2 + 1}}$$
B
$${R \over {\sqrt 2 + 1}}$$
C
$${{\sqrt 2 R} \over {\sqrt 2 - 1}}$$
D
$${R \over {\sqrt 2 - 1}}$$
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Two point charges q1$$\left( {\sqrt {10} \mu C} \right)$$ and q2($$-$$ 25 $$\mu$$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take $${1 \over {4\pi { \in _0}}}$$ = 9 $$\times$$ 109 Nm2C$$-$$2]
A
$$\left( {63\widehat i - 27\widehat j} \right) \times {10^2}$$
B
$$\left( { - 63\widehat i + 27\widehat j} \right) \times {10^2}$$
C
$$\left( {81\widehat i - 81\widehat j} \right) \times {10^2}$$
D
$$\left( { - 81\widehat i + 81\widehat j} \right) \times {10^2}$$
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Charge is distributed within a sphere of radius R with a volume charge density $$\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :
A
a log $$\left( {1 - {Q \over {2\pi aA}}} \right)$$
B
$${a \over 2}$$ log $$\left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)$$
C
a log $$\left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)$$
D
$${a \over 2}$$ log $$\left( {1 - {Q \over {2\pi aA}}} \right)$$
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