Tag: magnetic field lines due to current

Direction of magnetic field lines around a current carrying conductor can be found by RIght Hand Thumb Rule.

According to the Biot Savart's law, a current carrying conductor produces a magnetic field in its surroundings. This will cause the helix to oscillate across a mean position.

A charged particle produces an electric field around it independent of its motion. But when it is at rest, it doesn't produce a magnetic field. 

According to the right-hand thumb rule, the magnetic field lines around a long straight current-carrying conductor are concentric circles centered on the wire.

Coulombic force between two charges is given by

F=1/4π€ (q'.q″/r²)

From here, the SI UNIT of permittivity comes out is

= coulomb²/Newton-meter²

C²/N-m²

According to Biot-Savart's law, the magnetic field
$\displaystyle \overset{\rightarrow}{B} = \frac{\mu _o}{4 \pi} . \frac{q (\overset{\rightarrow}{v} \times \overset{\rightarrow}{r} ) }{r^3}$
The direction of $\overset{\rightarrow}{B}$ will be along $\overset{\rightarrow}{v} \times \overset{\rightarrow}{r}$ i.e. perpendicular to the plane containing $\overset{\rightarrow}{v}$ and $\overset{\rightarrow}{r}$.

Magnetic field produced by charges moving with velocity $\bar v$, at a distance r is $ \bar B$ = $\left ( \dfrac{\mu _0}{4\pi } \right )$.q$\dfrac{\bar v \times \hat r}{r^2}$
Therefore $\bar B \perp \bar v$

The particle moves in a circular path in a magnetic field. The radius of the path is r = v0 / (alpha * B0). Since it starts at the origin and moves along the x-axis, it reaches (0, y, 0) after completing a semicircle, so y = 2r = 2 * v0 / (alpha * B0).