选择擅长的领域继续答题？
{@each tagList as item}
${item.tagName}
{@/each}
手机回答更方便，互动更有趣，下载APP
提交成功是否继续回答问题？
手机回答更方便，互动更有趣，下载APP
展开全部
高斯定理是基本定理任何时候都是成立的
',getTip:function(t,e){return t.renderTip(e.getAttribute(t.triangularSign),e.getAttribute("jubao"))},getILeft:function(t,e){return t.left+e.offsetWidth/2-e.tip.offsetWidth/2},getSHtml:function(t,e,n){return t.tpl.replace(/\{\{#href\}\}/g,e).replace(/\{\{#jubao\}\}/g,n)}},baobiao:{triangularSign:"data-baobiao",tpl:'{{#baobiao_text}}',getTip:function(t,e){return t.renderTip(e.getAttribute(t.triangularSign))},getILeft:function(t,e){return t.left-21},getSHtml:function(t,e,n){return t.tpl.replace(/\{\{#baobiao_text\}\}/g,e)}}};function l(t){return this.type=t.type
"defaultTip",this.objTip=u[this.type],this.containerId="c-tips-container",this.advertContainerClass=t.adSelector,this.triangularSign=this.objTip.triangularSign,this.delaySeconds=200,this.adventContainer="",this.triangulars=[],this.motherContainer=a("div"),this.oTipContainer=i(this.containerId),this.tip="",this.tpl=this.objTip.tpl,this.init()}l.prototype={constructor:l,arrInit:function(){for(var t=0;t0}});else{var t=window.document;n.prototype.THROTTLE_TIMEOUT=100,n.prototype.POLL_INTERVAL=null,n.prototype.USE_MUTATION_OBSERVER=!0,n.prototype.observe=function(t){if(!this._observationTargets.some((function(e){return e.element==t}))){if(!t
1!=t.nodeType)throw new Error("target must be an Element");this._registerInstance(),this._observationTargets.push({element:t,entry:null}),this._monitorIntersections(),this._checkForIntersections()}},n.prototype.unobserve=function(t){this._observationTargets=this._observationTargets.filter((function(e){return e.element!=t})),this._observationTargets.length
(this._unmonitorIntersections(),this._unregisterInstance())},n.prototype.disconnect=function(){this._observationTargets=[],this._unmonitorIntersections(),this._unregisterInstance()},n.prototype.takeRecords=function(){var t=this._queuedEntries.slice();return this._queuedEntries=[],t},n.prototype._initThresholds=function(t){var e=t
[0];return Array.isArray(e)
(e=[e]),e.sort().filter((function(t,e,n){if("number"!=typeof t
isNaN(t)
t1)throw new Error("threshold must be a number between 0 and 1 inclusively");return t!==n[e-1]}))},n.prototype._parseRootMargin=function(t){var e=(t
"0px").split(/\s+/).map((function(t){var e=/^(-?\d*\.?\d+)(px|%)$/.exec(t);if(!e)throw new Error("rootMargin must be specified in pixels or percent");return{value:parseFloat(e[1]),unit:e[2]}}));return e[1]=e[1]
e[0],e[2]=e[2]
e[0],e[3]=e[3]
e[1],e},n.prototype._monitorIntersections=function(){this._monitoringIntersections
(this._monitoringIntersections=!0,this.POLL_INTERVAL?this._monitoringInterval=setInterval(this._checkForIntersections,this.POLL_INTERVAL):(r(window,"resize",this._checkForIntersections,!0),r(t,"scroll",this._checkForIntersections,!0),this.USE_MUTATION_OBSERVER&&"MutationObserver"in window&&(this._domObserver=new MutationObserver(this._checkForIntersections),this._domObserver.observe(t,{attributes:!0,childList:!0,characterData:!0,subtree:!0}))))},n.prototype._unmonitorIntersections=function(){this._monitoringIntersections&&(this._monitoringIntersections=!1,clearInterval(this._monitoringInterval),this._monitoringInterval=null,i(window,"resize",this._checkForIntersections,!0),i(t,"scroll",this._checkForIntersections,!0),this._domObserver&&(this._domObserver.disconnect(),this._domObserver=null))},n.prototype._checkForIntersections=function(){var t=this._rootIsInDom(),n=t?this._getRootRect():{top:0,bottom:0,left:0,right:0,width:0,height:0};this._observationTargets.forEach((function(r){var i=r.element,a=o(i),c=this._rootContainsTarget(i),s=r.entry,u=t&&c&&this._computeTargetAndRootIntersection(i,n),l=r.entry=new e({time:window.performance&&performance.now&&performance.now(),target:i,boundingClientRect:a,rootBounds:n,intersectionRect:u});s?t&&c?this._hasCrossedThreshold(s,l)&&this._queuedEntries.push(l):s&&s.isIntersecting&&this._queuedEntries.push(l):this._queuedEntries.push(l)}),this),this._queuedEntries.length&&this._callback(this.takeRecords(),this)},n.prototype._computeTargetAndRootIntersection=function(e,n){if("none"!=window.getComputedStyle(e).display){for(var r,i,a,s,u,l,f,h,p=o(e),d=c(e),v=!1;!v;){var g=null,m=1==d.nodeType?window.getComputedStyle(d):{};if("none"==m.display)return;if(d==this.root
d==t?(v=!0,g=n):d!=t.body&&d!=t.documentElement&&"visible"!=m.overflow&&(g=o(d)),g&&(r=g,i=p,a=void 0,s=void 0,u=void 0,l=void 0,f=void 0,h=void 0,a=Math.max(r.top,i.top),s=Math.min(r.bottom,i.bottom),u=Math.max(r.left,i.left),l=Math.min(r.right,i.right),h=s-a,!(p=(f=l-u)>=0&&h>=0&&{top:a,bottom:s,left:u,right:l,width:f,height:h})))break;d=c(d)}return p}},n.prototype._getRootRect=function(){var e;if(this.root)e=o(this.root);else{var n=t.documentElement,r=t.body;e={top:0,left:0,right:n.clientWidth
r.clientWidth,width:n.clientWidth
r.clientWidth,bottom:n.clientHeight
r.clientHeight,height:n.clientHeight
r.clientHeight}}return this._expandRectByRootMargin(e)},n.prototype._expandRectByRootMargin=function(t){var e=this._rootMarginValues.map((function(e,n){return"px"==e.unit?e.value:e.value*(n%2?t.width:t.height)/100})),n={top:t.top-e[0],right:t.right+e[1],bottom:t.bottom+e[2],left:t.left-e[3]};return n.width=n.right-n.left,n.height=n.bottom-n.top,n},n.prototype._hasCrossedThreshold=function(t,e){var n=t&&t.isIntersecting?t.intersectionRatio
0:-1,r=e.isIntersecting?e.intersectionRatio
0:-1;if(n!==r)for(var i=0;i0&&function(t,e,n,r){var i=document.getElementsByClassName(t);if(i.length>0)for(var o=0;o展开全部非闭合曲面下不适用。
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
为你推荐：
下载百度知道APP，抢鲜体验使用百度知道APP，立即抢鲜体验。你的手机镜头里或许有别人想知道的答案。扫描二维码下载
×个人、企业类侵权投诉
违法有害信息,请在下方选择后提交
类别色情低俗
涉嫌违法犯罪
时政信息不实
垃圾广告
低质灌水
我们会通过消息、邮箱等方式尽快将举报结果通知您。说明
做任务开宝箱累计完成0
个任务
10任务
50任务
100任务
200任务
任务列表加载中...

选择擅长的领域继续答题？
{@each tagList as item}
${item.tagName}
{@/each}
手机回答更方便，互动更有趣，下载APP
提交成功是否继续回答问题？
手机回答更方便，互动更有趣，下载APP
展开全部理论上可以，但在技巧层面，要具体求出明确的解析式，就要打开积分号，这就要求电荷的分布和高斯面是规则的。
本回答由提问者推荐已赞过已踩过你对这个回答的评价是？评论
收起
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
为你推荐：
下载百度知道APP，抢鲜体验使用百度知道APP，立即抢鲜体验。你的手机镜头里或许有别人想知道的答案。扫描二维码下载
×个人、企业类侵权投诉
违法有害信息,请在下方选择后提交
类别色情低俗
涉嫌违法犯罪
时政信息不实
垃圾广告
低质灌水
我们会通过消息、邮箱等方式尽快将举报结果通知您。说明
做任务开宝箱累计完成0
个任务
10任务
50任务
100任务
200任务
任务列表加载中...

对于矢量场 \boldsymbol A ，有熟知的Gauss定理和Stokes定理：\iiint \boldsymbol \nabla \cdot \boldsymbol A \bm dV=\iint \boldsymbol A\cdot d\boldsymbol S
(1)\oint \boldsymbol A\cdot d \boldsymbol l=\iint \boldsymbol \nabla\times\boldsymbol A \cdot d\boldsymbol S
(2)考虑标量场 \varphi 和一个任意的常矢量 \boldsymbol T ，将 \varphi\boldsymbol T 视为一个矢量场，应用（1），有：\begin{eqnarray} \iiint \boldsymbol \nabla \cdot(\varphi \boldsymbol T)dV &=&\iiint (\boldsymbol\nabla\varphi\cdot\boldsymbol T+\varphi\boldsymbol\nabla\cdot \boldsymbol T)dV \nonumber \\ &=&\left(\iiint \boldsymbol\nabla\varphi dV
\right)\cdot\boldsymbol T\nonumber \\ &=&\iint\varphi\boldsymbol T\cdot d\boldsymbol S\nonumber \\ &=&\left(\iint\varphi d\boldsymbol S\right)\cdot \boldsymbol T \end{eqnarray} (3)比较(3)式第2个等号和第4个等号，注意到 \boldsymbol T 的任意性，有：\iiint \boldsymbol\nabla\varphi dV=\iint\varphi d\boldsymbol S
(4)(4)式可当作标量场的“Gauss定理”。再将 \varphi\boldsymbol T 应用到(2)式中：\begin{eqnarray} \left(\oint\varphi d\boldsymbol l\right)\cdot \boldsymbol T &=&\oint\varphi\boldsymbol T\cdot d\boldsymbol l\\ &=&\iint\left(\boldsymbol\nabla\varphi\times\boldsymbol T+\varphi\boldsymbol\nabla\times\boldsymbol T\right)d\boldsymbol S\\ &=&\iint\boldsymbol\nabla\varphi\times\boldsymbol T\cdot d\boldsymbol S \\ &=&-\left(\iint\boldsymbol\nabla\varphi\times
d\boldsymbol S \right)\cdot \boldsymbol T \end{eqnarray}
(5)同样是注意到 \boldsymbol T 的任意性后，有：\oint\varphi d\boldsymbol l=-\iint\boldsymbol\nabla\varphi\times d\boldsymbol S
(6)(6)式可当作标量场的“Stokes定理”。一个简单应用[1]：稳恒电流环的磁矢势：\boldsymbol A(\boldsymbol r)=\frac{\mu_0I}{4\pi}\oint \frac{d\boldsymbol l'}{|\boldsymbol r-\boldsymbol r'|} 带撇的是源点，不带撇的是场点。考虑
\boldsymbol r|\gg
\boldsymbol r'
进行多极展开，零阶项为0，一阶项为：\begin{eqnarray} \boldsymbol A_{dip}(\boldsymbol r)&=&\frac{\mu_0I}{4\pi r^2}\oint r'\cos \theta' d\boldsymbol l' \\ &=&\frac{\mu_0 I}{4\pi r^2}\oint (\hat{\boldsymbol r }\cdot\boldsymbol r')d\boldsymbol l' \\ &=&-\frac{\mu_0 I}{4\pi r^2}\iint \boldsymbol\nabla'(\hat{\boldsymbol r }\cdot\boldsymbol r')\times d\boldsymbol S' \\ &=& -\frac{\mu_0 I}{4 \pi r^2}\iint\left(\hat{\boldsymbol r}\times(\boldsymbol \nabla'\times\boldsymbol r')+(\hat{\boldsymbol r}\cdot \boldsymbol \nabla')\boldsymbol r'\right)\times d \boldsymbol S '\\ &=&-\frac{\mu_0I}{4\pi r^2}\iint\hat{\boldsymbol r}\times d\boldsymbol S' \\ &=&\frac{\mu_0}{4\pi}\frac{I\boldsymbol S'\times\hat{r}}{r^2} \end{eqnarray} ^Griffiths电动力学原版第三版P244