1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -
A
$${{{Q_2}} \over {4\pi {\varepsilon _0}}}$$
B
$${{{Q^2}} \over {2\sqrt 2 \pi {\varepsilon _0}}}$$
C
$${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 3 }}} \right)$$
D
$${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 5 }}} \right)$$
2
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = $$\left( {{y \over 3}} \right)$$, the force on Q will be close to - $$\left( {{y \over 3} > > 2a} \right)$$

A
9F
B
3F
C
F/3
D
27F
3
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
$${{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$$
4
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
$${R \over {\sqrt 2 - 1}}$$
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