1
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
$$\sqrt {{2 \over m}} {\left( {{4 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$$
2
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
$$E \propto {1 \over D^2}$$
3
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
$${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} + {2{qQd} \over {{D^2}}}} \right]$$
4
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-
A
$$v \propto \left( {{r \over {{r_0}}}} \right)$$
B
$$v \propto \ln \left( {{r \over {{r_0}}}} \right)$$
C
$$v \propto {e^{ + r/{r_0}}}$$
D
$$v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)}$$
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