工程电磁场

如何描述线1周围的用来决定对线2作用力的力场？

Note that in the third case (perpendicular currents), I2 is in the same direction as H, so that their cross product (and the resulting force) is zero. The actual force computation involves a different field quantity, B, which is related to H through B = μ0H in free space. This will be taken up in a later lecture. Our immediate concern is how to find H from any given current distribution.

第三种情况，磁场与电流平行，叉乘=0

特别注意与距离的平方成反比, 而且叉矢量指向纸内（右手螺旋法则决定）Note the similarity to Coulomb’s Law

a point charge of magnitude dQ1at Point 1 would generate electric field at Point 2 given by:

The units of H are [A/m]

To determine the total field arising from the closed circuit path,

we sum the contributions from the current elements that make up

the entire loop, or

The contribution to the field at P from any portion of the current will be just the above integral evalated over just that portion.

..and so the differential current quantity that

appears in the Biot-Savart law becomes:

The magnetic field arising from a current

sheet is thus found from the two-dimensional

form of the Biot-Savart law:

of three-dimensional current elements, and so the Biot-Savart

and so..

so that:

Integrate this over the entire wire:

..after carrying out the cross product

Example: concluded

finally:

Current is into the page.

Magnetic field streamlines

are concentric circles, whose magnitudes

decrease as the inverse distance from the 线是如何画？（力线疏密反应强

如何画？

定值

/ρ 2，所以，磁力线的间隔怎么画？

..after a few additional steps (see Problem 7.8), we find:

carry out the cross products to find:

but we must include the angle dependence in the radial

unit vector注意:rho的单位矢量不是常量！！！

with this substitution, the radial component will integrate to zero, meaning that all radial components will cancel on the z axis. rho分量消了，仅仅z分量

Note the form of the numerator: the product of

the current and the loop area. We define this as

the magnetic moment:

环可定义磁矩

似偶极矩的定义

横向涡旋磁场

路径a和b的磁场环流= 总电流I

路径c的磁场环流= 总电流I的一部分

ρ

so that:as before.

solid conductors that carry equal and opposite

currents, I.

The line is assumed to be infinitely long, and the

circular symmetry suggests that

φ-directed, and will vary only with radius

Our objective is to find the magnetic field

for all values of ρ

无限长

内外导体等量异向电流

仅沿rho变化的phi向磁场

求全径向磁场分布

导体间磁场

内导体可看作无限长线电流束

考虑1、2处的电流丝产生的磁场叠加

仅phi向存在

ab间场直接为