1
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
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :
A
$$\sqrt {{2 \over m}} {\left( {{2 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$$
B
$$\sqrt {{2 \over m}} {\left( {{1 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$$
C
$$\sqrt {{2 \over m}} {\left( {{1 \over {5}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$$
D
$$\sqrt {{2 \over m}} {\left( {{4 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$$
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
Four point charges –q, +q, +q and –q are placed on y-axis at y = –2d, y = –d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as :-
A
$$E \propto {1 \over D^3}$$
B
$$E \propto {1 \over D}$$
C
$$E \propto {1 \over D^4}$$
D
$$E \propto {1 \over D^2}$$
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
A system of three charges are placed as shown in the figure :

If D >> d, the potential energy of the system is best given by :
A
$${1 \over {4\pi {\varepsilon _0}}}\left[ { {{{q^2}} \over d} + {{qQd} \over {{D^2}}}} \right]$$
B
$${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {2{D^2}}}} \right]$$
C
$${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {{D^2}}}} \right]$$
D
$${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} + {2{qQd} \over {{D^2}}}} \right]$$
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