[amp_mcq option1=”-2″ option2=”2″ option3=”1″ option4=”0″ correct=”option4″]<\/p>\n
The correct answer is $\\boxed{0}$.<\/p>\n
The divergence of a vector field is defined as the sum of the partial derivatives of the field’s components with respect to the coordinates. In this case, the vector field is $\\text{A} = krn$, where $r$ is the radial distance from the origin and $k$ is a constant. The partial derivatives of $r^n$ with respect to $x$, $y$, and $z$ are $nr^{n-1}x$, $nr^{n-1}y$, and $nr^{n-1}z$, respectively. Therefore, the divergence of $\\text{A}$ is<\/p>\n
$$\\nabla \\cdot \\text{A} = \\frac{\\partial}{\\partial x} (kr^n) + \\frac{\\partial}{\\partial y} (kr^n) + \\frac{\\partial}{\\partial z} (kr^n) = nkr^{n-1}.$$<\/p>\n
Setting this equal to zero and solving for $n$, we find that $n=0$.<\/p>\n
The other options are incorrect because they do not satisfy the equation $\\nabla \\cdot \\text{A} = 0$. For example, if $n=-2$, then the divergence of $\\text{A}$ is $2kr^{-1}$, which is not equal to zero.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”-2″ option2=”2″ option3=”1″ option4=”0″ correct=”option4″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20267","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n