Magnetism
Magnetic Field
A moving charge causes a magnetic 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.
Any component going along the direction of current is cancelled by cross product. Something else. Therefore, it is unsurprising that magnetic field is circulating.
Special Field: Wire
- TODO: Later fill out <01-03-24, xydxydxyd1> -
Loops
Let there be a loop of current flowing clockwise. The magnetic field inside the loop is always going out of the page, whereas the field outside always go into the page.
This can be proven by considering each single length of wire. The shape of the loop does not matter.
Ampere's Law of Magnetic 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 \oint_C \vec{B} \cdot d \vec{l} = \oint_C \left( \frac{\mu_0 I}{2 \pi \rho} \cdot d \vec{l} \right) = \mu_0 I }
