1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The two thin coaxial rings, each of radius 'a' and having charges +Q and $$-$$Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :
A
$${Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$$
B
$${Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$$
C
$${Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$$
D
$${Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$$
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $$\overrightarrow E$$ as a function of distance r from centre O is given by

A
B
C
D
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?

A
$${1 \over {4\pi {\varepsilon _0}}}{q \over {{l^2}}}$$
B
$${1 \over {4\pi {\varepsilon _0}}}{q \over {(2{l^2})}}\left( {2\sqrt 2 - 1} \right)$$
C
$${q \over {4\pi {\varepsilon _0}{{(2l)}^2}}}$$
D
$${1 \over {4\pi {\varepsilon _0}}}{{2q} \over {2{l^2}}}\left( {\sqrt 2 } \right)$$
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$$\theta$$' with the vertical?
A
$$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 2}}}$$
B
$$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 3}}}$$
C
$$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}g}}} \right)^{{1 \over 3}}}$$
D
$$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}{g^2}}}} \right)^{{1 \over 3}}}$$
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