1
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)
A
$${\left( {{{2{q^2}} \over {\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$$
B
$${\left( {{{{q^2}} \over {2\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$$
C
$${\left( {{{2\pi {\varepsilon _0}m{d^3}} \over {{q^2}}}} \right)^{{1 \over 2}}}$$
D
$${\left( {{{\pi {\varepsilon _0}m{d^3}} \over {2{q^2}}}} \right)^{{1 \over 2}}}$$
2
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :

A
$${{2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$$
B
$${{ - Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$$
C
$${Q \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$$
D
$${{ - 2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$$
3
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ and are held on the x axis at distance '$$a$$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :
A
$${p \over a}\sqrt {{3 \over {2\pi { \in _0}ma}}}$$
B
$${p \over a}\sqrt {{1 \over {\pi { \in _0}ma}}}$$
C
$${p \over a}\sqrt {{1 \over {2\pi { \in _0}ma}}}$$
D
$${p \over a}\sqrt {{2 \over {\pi { \in _0}ma}}}$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?
A
$${1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}} > F > 0$$ for r < R
B
$$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$$ for r > R
C
$$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$$ for all r
D
$$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}}$$ for r < R
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