1
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then
$${{{Q_1}} \over {{Q_2}}}$$ is proportional to :
A
$${{x_1^3} \over {x_2^3}}$$
B
$${{x_2^2} \over {x_1^2}}$$
C
$${{{x_1}} \over {{x_2}}}$$
D
$${{{x_2}} \over {{x_1}}}$$
2
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively.
(Take V = 0 at infinity)
A
V = 0; E = 0
B
$$V = {{10q} \over {4\pi {\varepsilon _0}R}}$$; $$E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}$$
C
$$V = {{10q} \over {4\pi {\varepsilon _0}R}}$$; E = 0
D
V = 0; $$E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}$$
3
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then :
(assume the remaining portion to be spherical).
A
v2 = $$y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$$
B
v2 = $$2y\left[ {{{qQR} \over {4\pi {\varepsilon _0}{{\left( {R + y} \right)}^3}m}} + g} \right]$$
C
v2 = $$2y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$$
D
v2 = $$y\left[ {{{qQ} \over {4\pi {\varepsilon _0}{R^2}ym}} + g} \right]$$
4
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
A particle of charge q and mass m is subjected to an electric field
E = E0 (1 – $$a$$x2) in the x-direction, where $$a$$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
A
$$a$$
B
$$\sqrt {{2 \over a}}$$
C
$$\sqrt {{3 \over a}}$$
D
$$\sqrt {{1 \over a}}$$
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