1
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center 0 of the hexagon and is bisected by the side. Which of the following statement(s) is(are) correct in SI units?

A
When $x=q$, the magnitude of the electric field at 0 is zero.
B
When $x=-q$, the magnitude of the electric field at 0 is $\frac{q}{6 \pi \epsilon_{o} a^{2}}$.
C
When $x=2 q$, the potential at 0 is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
D
When $x=-3 q$, the potential at 0 is $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1 An electric dipole with dipole moment $${{{p_0}} \over {\sqrt 2 }}(\widehat i + \widehat j)$$ is held fixed at the origin O in the presence of a uniform electric field of magnitude E0. If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are, ($$\in$$0 is the permittivity of the free space, R >> dipole size)
A
The magnitude of total electric field on any two points of the circle will be same.
B
Total electric field at point B is $${\overrightarrow E _B}$$ = 0
C
$$R = {\left( {{{{p_0}} \over {4\pi { \in _0}{E_0}}}} \right)^{1/3}}$$
D
Total electric field at point A is

$${\overrightarrow E _A} = \sqrt 2 {E_0}(\widehat i + \widehat j)$$
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
An infinitely long thin non-conducting wire is parallel to the $$z$$-axis and carries a uniform line charge density $$\lambda .$$ It pierces a thin non-conducting spherical shell of radius $$R$$ in such a way that the arc $$PQ$$ subtends an angle $${120^ \circ }$$ at the center $$O$$ of the spherical shell, as shown in the figure. The permittivity of free space is $${ \in _0}.$$ Which of the following statement is (are) true? A
The electric flux through the shell is $$\sqrt 3 R\lambda /{ \in _0}$$
B
The $$z$$-component of the electric field is zero at all the points on the surface of the shell
C
The electric flux through the shell is $$\sqrt 2 R\lambda /{ \in _0}$$
D
The electric field is normal to the surface of the shell at all points
4
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A point charge $$+Q$$ is placed just outside an imaginary hemispherical surface of radius $$R$$ as shown in the figure. Which of the following statements is/are correct? A
The electric flux passing through the curved surface of the hemisphere is

$$- {Q \over {2{\varepsilon _0}}}$$ $$\left( {1 - {1 \over {\sqrt 2 }}} \right)$$
B
Total flux through the curved and the flat surfaces is $${Q \over {{\varepsilon _0}}}$$
C
The component of the electric field normal to the flat surface is constant over the surface
D
The circumference of the flat surface is an equipotential
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