Question:
Consider a volume integral
\(I=\int_V\nabla^2(\frac{1}{r})dv\)
over a volume \( V \), where \( r = \sqrt{x^2 + y^2 + z^2} \). Which of the following statements is/are correct?
Consider a volume integral
\(I=\int_V\nabla^2(\frac{1}{r})dv\)
over a volume \( V \), where \( r = \sqrt{x^2 + y^2 + z^2} \). Which of the following statements is/are correct?
\(I=\int_V\nabla^2(\frac{1}{r})dv\)
over a volume \( V \), where \( r = \sqrt{x^2 + y^2 + z^2} \). Which of the following statements is/are correct?
Updated On: Jul 12, 2024
- The integrand vanishes for \( r \neq 0 \).
- The integrand vanishes for \( r \neq 0 \).
- \( I = 0 \), if \( r = 0 \) is not inside the volume \( V \).
- The integrand diverges as \( r \rightarrow \infty \).
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The Correct Option is A, B, C
Solution and Explanation
The correct options are (A) :\( I = -4\pi \), if \( r = 0 \) is inside the volume \( V \).(B):The integrand vanishes for \( r \neq 0 \).(C):\( I = 0 \), if \( r = 0 \) is not inside the volume \( V \).
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