1
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$.

A
$${Q \over {4\pi {\varepsilon _0}{L^2}}}$$
B
$${Q \over {3\pi {\varepsilon _0}{L^2}}}$$
C
$${Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}$$
D
$${{\sqrt 3 Q} \over {4\pi {\varepsilon _0}{L^2}}}$$
2
JEE Main 2021 (Online) 25th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E$$ through the shaded area is :

A
$${q \over {24{\varepsilon _0}}}$$
B
$${q \over {48{\varepsilon _0}}}$$
C
$${q \over {4{\varepsilon _0}}}$$
D
$${q \over {8{\varepsilon _0}}}$$
3
JEE Main 2021 (Online) 24th February Evening Slot
MCQ (Single Correct Answer)
+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
$${\left( {{{\pi {\varepsilon _0}m{d^3}} \over {2{q^2}}}} \right)^{{1 \over 2}}}$$
4
JEE Main 2021 (Online) 24th February Morning Slot
MCQ (Single Correct Answer)
+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
$${{ - 2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$$
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