1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2 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. 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 $\frac{13 \pi k}{\epsilon_{0}}$.
2
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2 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.
3
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 $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_{o} a}$.
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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