Ampere's Law

I want to find magnetic field generated by infinitly long wire using ampere's law but ampere's law is gives us scaler how can i get vectorial solutions

ampere's law : u0*i/(2*pi*d)

Answer 1

[Star Strider]

You may not have the definition of it that you need.

Try this:

mu0 = pi*4E-7;                                      % Ref: https://en.wikipedia.org/wiki/Vacuum_permeability
AmpereB = @(m0u,I,r) (mu0.*I)./(2*pi*r);            % µₒ = Magnetic Constant, I = Current (A), r = radius (m), Ref: https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law

radius = linspace(1E-3, 1);
I = 1;

figure(1)
semilogy(radius, AmpereB(mu0,I,radius))
grid
xlabel('r (m)')
ylabel('B')

[Sogogo]

thanks for your answer

but how can i get magnetic field vectors (arrows) arround the wire, how can i get directional arrows

[Star Strider]

These appear to have the correct directions (using conventional calculus to generate directional components for the quiver arrows):

mu0 = pi*4E-7;                                      % Ref: https://en.wikipedia.org/wiki/Vacuum_permeability
AmpereB = @(m0u,I,r) (mu0.*I)./(2*pi*r);            % µₒ = Magnetic Constant, I = Current (A), r = radius (m), Ref: https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law

radius = linspace(1E-3, 1);
I = 1;

figure(1)
semilogy(radius, AmpereB(mu0,I,radius))
grid
xlabel('r (m)')
ylabel('B')

thp = linspace(0, 2*pi);
thq = linspace(0, 2*pi, 10);
r5f = @(th) AmpereB(mu0,I,0.5)*[cos(th); sin(th)];      % Circle For Quiver Origins
uv = AmpereB(mu0,I,0.5)*[-sin(thq); cos(thq)];          % Quiver Directions
r5q = r5f(thq);                                         % Quiver Origins
r5c = r5f(thp);                                         % Continuous Circle

figure(2)
quiver(r5q(1,:), r5q(2,:), uv(1,:), uv(2,:))            % Plot Arrows
hold on
plot(r5c(1,:), r5c(2,:), '-r')                          % Plot Radius=0.5 Circle
hold off
grid
axis equal
title('B(r=0.5m, I=1A)')

This is the best I can do. I’ve not done anything with Ampere’s law since shortly before Pangaea split apart.

[Sogogo]

thank you very much i should keep working from this one

[Star Strider]

As always, my pleasure!