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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{B} (\vec{r}) = \frac{ \mu_0 }{ 4 \pi } \frac{ I_1 d\vec{l}_1 \times \hat{r}}{ r^2 } = \frac{ \mu_0 }{ 4 \pi } \frac{ \left| I dl \right| }{ r^3 } \rho \hat{e}_\phi }

Where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_0 } is magnetic permeability, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho } is distance from the wire.

Magnetic field of a current with right hand rule

Any component going along the direction of current is cancelled by cross product. Something else. Therefore, it is unsurprising that magnetic field is circulating.