物理学:安培定律和比奥-萨瓦特定律有什么区别?如何确定用于特定问题的哪一个?


回答 1:

ByapplyingAmperescircuitallawtoacurrentcarryingcircularcoil,choosingacircleofradiusaawhichissmallerthantheradiusofthecoil,andintegratingoverit,Ifoundthatmagneticfieldinsideacurrentcarryingcoiliszerosincethereisnocurrentenclosedwithinthecircle.SotherhsintheequationBdl=μ0I[math]Bdl=μ0I[/math]becomeszerowhicheffectivelymeansthemagneticfieldiszero.However,wealreadyknowthatbyusingBiotSavartslawwecaneasilyderivethatmagneticfieldatthecenterofacurrentcarryingcircularcoilis[math]B=μ0I2r[/math].By applying Ampere's circuital law to a current-carrying circular coil, choosing a circle of radius aawhich is smaller than the radius of the coil, and integrating over it, I found that magnetic field inside a current carrying coil is zero since there is no current enclosed within the circle. So the rhs in the equation ∮B⋅dl=μ0I[math]∮B⋅dl=μ0I[/math] becomes zero which effectively means the magnetic field is zero. However, we already know that by using Biot-Savart's law we can easily derive that magnetic field at the center of a current-carrying circular coil is [math]B=μ0I2r[/math].


回答 2:

高斯定律与安培定律的区别。

高斯定律和安培定律都可以使用,当高斯定律中的电荷分布对称和安培定律中的电流分布对称为球形,圆柱体,立方等时,也可以用于封闭曲面,在高斯定律中用虚构的高斯曲面确定电荷分布,并根据安培定律绘制一个(安培环)来确定电流分布。一个主要的区别是,外加电场中使用的高斯定律和外加磁场中使用的安培定律,意味着电流以对称分布流动。