Let $\vec { F } = \frac { x \vec { i } + y \vec { j } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } }$ .
True or False: The flux of $\vec { F }$ through any cylinder C (with $x ^ { 2 } + y ^ { 2 } = R ^ { 2 } , 0 \leq z \leq 1$ )does not depend on the radius R.

Question

Quizplus · Accepted Answer

The flux of $\vec { F }$ through any cylinder C (with $x ^ { 2 } + y ^ { 2 } = R ^ { 2 } , 0 \leq z \leq 1$ )does not depend on the radius R because the divergence of $\vec { F }$ is zero.

Let F⃗=xi⃗+yj⃗(x2+y2)3/2\vec { F } = \frac { x \vec { i } + y \vec { j } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } }F=(x2+y2)3/2xi+yj​​

Let $\vec { F } = \frac { x \vec { i } + y \vec { j } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } }$