Exploring B_x and B_y by 2d graphs

> L1:=[seq([(i-10.5)/10*0.02,Bx((i-10.5)/10*0.02,0.005)],i=1..20)]:

> plot(L1,title="B_x as a function of x (above the wire)");

> L1:=[seq([(i-10.5)/10*0.02,Bx((i-10.5)/10*0.02,-0.005)],i=1..20)]:

> plot(L1,title="B_x as a function of x (below the wire)");

Note the change in sign: above the wire and below the wire the transverse component of the magnetic field has opposite sign! This is the first step towards understanding that the field lines are closed curves around the wire. We can also show that the strength of the B_x component falls off with height. Due to the divergence of the function at z=0 we do not connect the points.

> L1:=[seq([(i-10.5)/10*0.005,Bx(0.005,(i-10.5)/10*0.005)],i=1..20)]:

> plot(L1,style=point,symbol=cross,title="B_x as a function of height (crossing the wire)");

For the z -component:

> L1:=[seq([(i-20.5)/20*0.04,Bz((i-20.5)/20*0.04,0.005)],i=1..40)]:

> plot(L1,title="B_z as a function of x (above the loop)");

We obtain a strong z-component for the magnetic field at the center of the loop. Outside of the current loop the direction of B_z is reversed.

> L1:=[seq([(i-20.5)/20*0.01,Bz((i-20.5)/20*0.01,0.0)],i=1..40)]:

> plot(L1,style=point,symbol=cross,title="B_z as a function of x (crossing the loop)");

In the immediate vicinity of the current wire B _ z diverges and changes sign, which is in analogy to the B _ x component's behaviour as a function of x .

At the center the field the field is nearly constant.

> L1:=[seq([(i-20.5)/20*0.02,Bz((i-20.5)/20*0.02,-0.001)],i=1..40)]:

> plot(L1,title="B_z as a function of x (just below the loop)");

> L1:=[seq([(i-20.5)/20*0.01,Bz(0.005,(i-20.5)/20*0.01)],i=1..40)]:

> plot(L1,title="B_z as a function of z (crossing the wire)");

> L1:=[seq([(i-20.5)/20*0.01,Bz(0.001,(i-20.5)/20*0.01)],i=1..40)]:

> plot(L1,title="B_z as a function of z (slightly off center)");