GATE EE 2022 Set 1 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumPoisson & Laplace EquationsElectrostaticsElectromagnetic Fields
Electromagnetic Fields → Electrostatics → Poisson & Laplace Equations
Last updated
Question
As shown in the figure below, two concentric conducting spherical shells, centered at and having radii and are maintained at potentials such that the potential at is and at is . Assume that depends only on , where is the radial distance. The expression for in the region between and is

Correct answer
(B) V(r) = (c d (V₁ - V₂))/((d - c) r) + (V₂ d - V₁ c)/(d - c)
Solution
The potential in a charge-free region between two concentric spherical shells satisfies Laplace's equation . In spherical coordinates, for a potential that depends only on the radial distance , this simplifies to:Integrating with respect to :Integrating again:Applying the boundary conditions:
1.At ,
2.At ,
Subtracting the second equation from the first:Now, solve for using the first boundary condition:Substituting and back into the general expression for :This matches option (B).Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Electrostatics
2026 Set 1 Q15A uniform ring charge of radius carries a total charge . Which one of the following options…2026 Set 1 Q16A positive point charge with velocity enters a region having electric field…2026 Set 1 Q51The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two…2026 Set 1 Q63A uniform spherical volume charge distribution of radius m, centered at the origin, has a…2025 Set 1 Q25Which one of the following figures represents the radial electric field distribution caused…