Magnetism

Magnetic Field

A moving charge causes a magetic field, following the right hand rule: Your thumb pointing towards the direction of movement of the positive charge, and your other fingers wrap around to indicate the direction of the magnetic field.

A circulating current forms a magnetic dipole.

Calculate Field

${\vec {B}}({\vec {r}})={\frac {\mu _{0}}{4\pi }}{\frac {I_{1}d{\vec {l}}_{1}\times {\hat {r}}}{r^{2}}}$

Any component going along the direction of current is cancelled by cross product. Something else. Therefore,

Unlike electric fields, there is no beginning or end to magnetic fields. Consider a close surface: The magnetic flux is always 0. $\oiint _{S}{\vec {B}}\cdot d{\vec {s}}=0\oint {\vec {B}}\cdot d{\vec {l}}\neq 0$

Recall that a point charge produces an electric field that points radially outward based on Coulomb's Law. This results in Gauss's Law and circulation being zero.