1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
A disk of radius $\mathrm{R}$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

$$ V(z)=\frac{\sigma}{2 \epsilon_{0}}\left(\sqrt{R^{2}+z^{2}}-z\right) . $$

A particle of positive charge $q$ is placed initially at rest at a point on the $z$ axis with $z=z_{0}$ and $z_{0}>0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F}=-c \hat{k}$ with $c>0$. Let $\beta=\frac{2 c \epsilon_{0}}{q \sigma}$.

Which of the following statement(s) is(are) correct?
A
For $\beta=\frac{1}{4}$ and $z_{0}=\frac{25}{7} R$, the particle reaches the origin.
B
For $\beta=\frac{1}{4}$ and $z_{0}=\frac{3}{7} R$, the particle reaches the origin.
C
For $\beta=\frac{1}{4}$ and $z_{0}=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_{0}$.
D
For $\beta>1$ and $z_{0}>0$, the particle always reaches the origin.
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

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.

JEE Advanced 2022 Paper 1 Online Physics - Electrostatics Question 17 English

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 $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
3
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
4
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
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 JEE Advanced 2020 Paper 1 Offline Physics - Electrostatics Question 33 English
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
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