1
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

A small electric dipole $\vec{p}_0$, having a moment of inertia $I$ about its center, is kept at a distance $r$ from the center of a spherical shell of radius $R$. The surface charge density $\sigma$ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle $\theta$ as shown in the figure. While staying at a distance $r$, the dipole is free to rotate about its center.

JEE Advanced 2024 Paper 2 Online Physics - Electrostatics Question 3 English

If released from rest, then which of the following statement(s) is(are) correct?

[ $\varepsilon_0$ is the permittivity of free space.]

A
The dipole will undergo small oscillations at any finite value of $r$.
B
The dipole will undergo small oscillations at any finite value of $r>R$.
C
The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{2 \sigma p_0}{\epsilon_0 I}}$ at $r=2 R$.
D
The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{\sigma p_0}{100 \epsilon_0 I}}$ at $r=10 R$.
2
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_{A}=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_{A}=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_{B}$, the electrostatic charge density varies as $\rho_{B}=$ $\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.

JEE Advanced 2022 Paper 2 Online Physics - Electrostatics Question 19 English

Which of the following statement(s) is(are) correct?

A
If $r_{B}=\sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside $B$.
B
If $r_{B}=\frac{3}{2}$, then the electric potential just outside $B$ is $\frac{k}{\epsilon_{0}}$.
C
If $r_{B}=2$, then the total charge of the configuration is $15 \pi k$.
D
If $r_{B}=\frac{5}{2}$, then the magnitude of the electric field just outside $B$ is $\frac{13 \pi k}{\epsilon_{0}}$.
3
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.
4
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 21 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 $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
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