Start free

Physics · Electrostatics

JEE Advanced 2019 — Paper 1 — Question 2

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0V_{0}. A hole with a small area α4πR2(α≪1)\alpha 4 \pi R^{2}(\alpha \ll 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

  1. Option A:

    The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R2 R from the center of the spherical shell will be reduced by αV02R\frac{\alpha V_{0}}{2 R}

  2. Option B:

    The magnitude of electric field at the center of the shell is reduced by αV02R\frac{\alpha V_{0}}{2 R}

  3. Option C:

    The ratio of the potential at the center of the shell to that of the point at 12R\frac{1}{2} \mathrm{R} from center towards the hole will be 1−α1−2α\frac{1-\alpha}{1-2 \alpha}

    Correct
  4. Option D:

    The potential at the center of the shell is reduced by 2α V02 \alpha \mathrm{~V}_{0}

Answer: C

Step-by-step solution

V0=σ4πR24πε0R⇒σ=V0ε0R\mathrm{V}_{0}=\frac{\sigma 4 \pi \mathrm{R}^{2}}{4 \pi \varepsilon_{0} \mathrm{R}} \Rightarrow \sigma=\frac{\mathrm{V}_{0} \varepsilon_{0}}{\mathrm{R}}

so V at R/2=v0−14πε02RV0ε0Rα4πR2=V0(1−2α)\mathrm{R} / 2=\mathrm{v}_{0}-\frac{1}{4 \pi \varepsilon_{0}} \frac{2}{\mathrm{R}} \frac{\mathrm{V}_{0} \varepsilon_{0}}{\mathrm{R}} \alpha 4 \pi \mathrm{R}^{2}=\mathrm{V}_{0}(1-2 \alpha)

and V at centre =V0−14πε01RV0ε0α4πR2R=V0(1−α)=\mathrm{V}_{0}-\frac{1}{4 \pi \varepsilon_{0}} \frac{1}{\mathrm{R}} \frac{\mathrm{V}_{0} \varepsilon_{0} \alpha 4 \pi \mathrm{R}^{2}}{\mathrm{R}}=\mathrm{V}_{0}(1-\alpha)

Answer key and solution verified before publishing.

Practise Electrostatics

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free
Exam
JEE Advanced 2019
Paper
Paper 1
Subject
Physics
Chapter
Electrostatics
Topic
Electrostatic Potential Energy and Electric Potential
A thin spherical insulating shell of radius R carries a uniformly… | JEE Advanced 2019 PYQ with Solution · DhiX AI