Pravegaa PYQ Series · Volume 1: Mathematical Physics

MP11: Dirac Delta and Green's Functions

20 previous-year questions with complete solutions, from IIT JAM, GATE, CSIR NET-JRF, JEST and TIFR, arranged from IIT JAM and GATE through to TIFR and from the most recent paper backwards. Click Show solution under any question.

IIT JAM: 1
GATE: 1
CSIR NET: 8
JEST: 6
TIFR GS: 4

MP11.1IIT JAM 2020, Q12MCQ | 2 marks

The volume integral \(\displaystyle\int_V e^{-\left(\frac{r}{R}\right)^2}\,\vec\nabla\cdot\left(\frac{\hat r}{r^2}\right)d^3r\), where \(V\) is the volume of a sphere of radius \(R\) centered at the origin, is equal to

\(4\pi\)
\(0\)
\(\dfrac43\pi R^3\)
\(1\)

Show solution

Since \(\vec\nabla\cdot\left(\dfrac{\hat r}{r^2}\right)=4\pi\,\delta^3(\vec r)\), \[ \int_V e^{-r^2/R^2}\,4\pi\,\delta^3(\vec r)\,d^3r=4\pi\,e^{0}=\boxed{4\pi} \] since the origin lies inside \(V\).

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Chapter 11 Dirac Delta and Green’s Functions Previous Year Questions with Solutions

MP11: Dirac Delta and Green's Functions

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