ELECTROSTATICS_JEE-Advanced-2022_S2 - Competishun – Live JEE & NEET Courses and Exam Prep

JEE Advance2022

Paper-2

Multiple correct answers - Select all that apply

Question

A disk of radius 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 $\beta=\frac{2 c \varepsilon_0}{q \sigma}$. Which of the following statement(s) is(are) correct?

Select ALL correct options:

For $\beta=\frac{1}{4}$ and $z_0=\frac{25}{7} R$, the particle reaches the origin.

For $\beta=\frac{1}{4}$ and $z_0=\frac{3}{7} R$, the particle reaches the origin.

For $\beta=\frac{1}{4}$ and $z_0=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_0$

For $\beta>\frac{1}{4}$ and $z_0>0$, the particle always reaches the origin.

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution