基于 Biot-Savart 定律模拟电流回路的磁场附matlab代码

Magnetic field of coils

Profiles the magnetic field along a selectable curve for a helical (solenoidal or toroidal) current loop using the

Biot-Savart law. The Biot-Savart line integral is represented first symbolically in terms of a parametric path in

three dimensions, then converted to a function of the parameter and integrated numerically. The results are

compared to analytic results for an ideal solenoid or toroid.

Author: D. Carlsmith

Table of Contents

Introduction...............................................................................................................................................................1

Initialize.....................................................................................................................................................................2

Try this: Change the range of the number of turns in the coil. .............................................................................3

Loop over number of turns in the coil....................................................................................................................... 3

Create symbolic expression for magnetic field integrand......................................................................................... 3

Plot the current loop in 3d space.............................................................................................................................. 4

Try this: Change toroidal sampling line radius to sample elsewhere within, exterior to, or interior to the torus....

5

Loop over field points along the profile line parallel to the -axis and compute ........................................................ 6

Loop over field components and perform integration over current. ......................................................................... 6

Plot field components along sampling curve. .......................................................................................................... 7

Try this: For the solenoid, compare the vertical line z-component to the exact axial field of an ideal coil...........7

the vector line integral into an integral over the parameter t. The vector derivative is tangential to the

circuit.

The magnetic field within a helical coil of length L and number of turns Ncentered on the z-axis, for

and constant can be found using found using Ampere's law. It is uniform and axial and has magnitude

.

1

For an ideal toroidal current distribution of inner radius and outer radius , Ampere's Law applied to a circle

of radius r with implies

.

The field outside an ideal solenoidal or toridal coil vanishes. These analytic results serve as reference values

which may be approached for high density windings.

Set some default numerical values for current. SI units are used throughout.

Try this: Change the pitch Loopstep of the helix to see the impact on the central field

Try this: Change the sampling distance Zstep to create a smoother plot of the variation

along the sampling line.

Set transverse coordinates of line parallel to the z-axis along which we find the field.

Try this: Change the transverse coordinates of the sampling line to profile the magnetic

field along your choice of line parallel to the solenoid axis.

2

Try this: Replace the solenoidal field with a toroidal winding.

The value torus=1 switches torus on. The value torus=0 switches torus off. For the toriodal current, the field

Initialize linewidth for displaying circuit elements.

Create a collection of Nturn values.

Try this: Change the range of the number of turns in the coil.

Stick with just a few choices total for distinguishable linewidths when the coils are superposed in the first plot.

Construct the factor , proportional to the electric field of the charges in the current element, which appears

in the Biot-Savart Law.

3