Chapter#2: Single Particle Motion

All Short Questions of Single Particle Motion for the book Plasma Physics for BS/MSc Physics students.

Q.2.1 what will be cyclotron frequency of electron if the magnetic field of chamber is 2 Tesla.

Answer: Formula of cyclotron frequency;

$\omega_c=\ \frac{-eB}{m_e}$

$e=1.6\times{10}^{-19}J$

$m_e=9.1\times{10}^{31}Kg$

By putting values in formula;

$\omega_c=\ \frac{(-1.6\times{10}^{-19})(2)}{9.1\times{10}^{31}}$

$\omega_c=\ \frac{-3.2\times{10}^{-19}}{9.1\times{10}^{31}}$

$\omega_c=3.5\times{10}^{-51\ }$

Q.2.2 Write down the verification conditions of curvature drift.

Answer: There are two verification conditions of curvature drift.

$\overline{\mathrm{\nabla}}\ .\ \overline{B}=0$
$\overline{\mathrm{\nabla}}\ \times\ \overline{B}=0$

Q.2.3 Prove that
$\overline{\nabla}\ .\ \overline{B}=0$

Answer:

$\overline{\mathrm{\nabla}}$ is written in cylindrical coordinates because, we have r and θ components.

$\frac{1}{r}\ \frac{\partial}{\partial r}\ \left(rBr\right)+\ \frac{1}{r}\ \frac{\partial B\theta}{\partial\theta}+\ \frac{\partial Bz}{\partial z}=0$

$\frac{1}{r}\ \frac{\partial B\theta}{\partial\theta}=0$

$\frac{1}{r}\ \neq0$ Then $\frac{\partial B\theta}{\partial\theta}=0$ and $B_\theta$ = constant with respect to ‘θ’.

$\overline{\mathrm{\nabla}}.\ \overline{B}=0$ It means monopoles does not exist.

Q.2.4 what is meant by Larmour radius. Also write its expression.

Answer: Larmour radius is also known as gyro radius, radius of gyration or cyclotron radius. The radius of circular motion of a charged particle in the presence of a uniform magnetic field.

$r_L=\ mV⟂qB$

Q.2.5 Write down the factors on which current density of ions and electrons depends?

Answer: Current density of ions and electrons depends upon “density of plasma and strength of magnetic field”

Q.2.6 what is the relation between magnetic and gravitational drift?

Answer: If force in magnetic drift is gravitational force then the drift is called gravitational drift.

$F=mg$

Magnetic drift ${\ V}_{gc}=\ \frac{F\times B}{qB^2}$

Gravitational drift; $V_{gc}=\frac{mg\ \times B}{qB^2}$

Q.2.7 why trajectory of charged particle in space is helix?

Answer: The direction of motion is always such that the magnetic field generated by charged particle is opposite to externally imposed field. Therefore plasma particles tend to reduce the and plasma are diamagnetic. The trajectory of the charged particle in space is helix.