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 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $$\alpha$$. The spheres are now immersed in a dielectric liquid of density 800 kg m$$-$$3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then
A
electric force between the spheres remains unchanged
B
electric force between the spheres reduces
C
mass density of the spheres is 840 kg m$$-$$3
D
the tension in the strings holding the spheres remains unchanged
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A uniform electric field, $$\overrightarrow E = - 400\sqrt 3 \widehat y$$ NC−1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2$$\sqrt {10}$$ $$\times$$ 106 ms−1 . This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure.
Take $${q \over m}$$ = 1010 Ckg−1 . Then
A
the particle will hit T if projected at an angle 45o from the horizontal
B
the particle will hit T if projected either at an angle 30o or 60o from the horizontal
C
time taken by the particle to hit T could be $$\sqrt {{5 \over 6}}$$ $$\mu$$s as well as $$\sqrt {{5 \over 2}}$$ $$\mu$$s
D
time taken by the particle to hit T is $$\sqrt {{5 \over 3}}$$ $$\mu$$s
4
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

$${\overrightarrow E _A} = \sqrt 2 {E_0}(\widehat i + \widehat j)$$
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