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?

• A. The integrand vanishes for \( r \neq 0 \).
• B. The integrand vanishes for \( r \neq 0 \).
• C. \( I = 0 \), if \( r = 0 \) is not inside the volume \( V \).
• D. The integrand diverges as \( r \rightarrow \infty \).

Answer 1

The Correct Option is A, B, C

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 \( V \).