Question

If \[ \mathbf{F}=ax\mathbf{i}+by\mathbf{j}+cz\mathbf{k}, \] where \(a\), \(b\), and \(c\) are constants, and \(S\) is the surface of the unit sphere, then \[ \iint_{S}\mathbf{F}\cdot\mathbf{n}\,dS=\_ \]

• A. $4\pi/3(a + b + c)$
• B. $4\pi(a + b + c)$
• C. $2\pi/3(a + b + c)$
• D. $\pi(a + b + c)$

Hint:

Use Gauss Divergence Theorem to convert a complex surface integral into a simple volume integral whenever the surface is closed.

Answer 1

The Correct Option is A