JEE Main 2019PhysicsElectrostaticsMediumMCQ

JEE Main 2019 — Electrostatics Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

Charge is distributed within a sphere of radius R with a volume charge density ρr=Ar2e-2ra, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:

Choose an option

Show full solutionCorrect option: A
Correct answer
Aa2log⁡11-Q2πaA

Step-by-step explanation

ρr=Ar2 e-2ra



Charge enclosed between r and r+dr is

dq=ρr 4πr2dr

To get total charge Q

Q=∫0Rdq=∫0RAr2e-2r/a 4πr2dr=-4πAa2[e-2r/a]0R

Q=-4π Aa2e-2R/a-1

R=-ln⁡1-Q24πAaa2=a2ln⁡11-Q2πaA

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About this question

This is a previous-year question from JEE Main 2019, covering the Electrostatics chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.