91Ó°ÊÓ

The magnetic field is described as a region that is around a particular magnetic material or moving charge in which the magnetic force acts. The magnetic field is beneficial for distributing a magnetic force inside a magnetic material.

The equation of the angular momentum of a particle is expressed as:

$L=∫\frac{\mathrm{dL}}{\mathrm{dt}}\mathrm{dt}$

The above equation can also be reduced as:

$$\begin{gathered} ∫\frac{dL}{dt}dt=∫Ndt \\ =∫\left(r×F\right)dt \\ =∫\left(r×q\right)(v×B))dt \\ =\mathrm{q}∫r×(dl×B) \end{gathered}$$

Hence, further as:

$$\begin{gathered} ∫\frac{dL}{dt}dt=q∫r×(dl×B) \\ =q\left[∫(r.B)dl-∫B(r.dl)\right] \end{gathered}$$

…(¾±)

As is mainly perpendicular to B , Hence,$r.B=0$.

The equation of the product of the distance and the increase in the length is expressed as:

$$\begin{gathered} r.dl=r.dr \\ =\frac{1}{2}d(r.r) \\ =\frac{1}{2}d{r}^2 \\ =rdr \end{gathered}$$

Hence, further as:

$r.dl=\left(\frac{1}{2\mathrm{Ï€}}\right)2\mathrm{Ï€}rdr$

Substitute the above value in equation (i).

$$\begin{gathered} L=\frac{q}{2\mathrm{π}}{∫}_0^{R}B2\mathrm{π}rdr \\ =-\frac{q}{2\mathrm{π}}∫Bda \\ =-\frac{q}{2\mathrm{π}}\mathrm{Φ} \end{gathered}$$

Hence, as$\mathrm{Φ}=0$ , then the value of the angular momentum is L=0.

Thus, a charged particle that starts out at the center will emerge from the field region on a radial path, is proved.