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.
Q.2.8 Describe the condition that is required for charged gas to be plasma?
Answer: For single particle motion there are following three conditions.
- Particles does not interact with each other.
- No relativistic effect are considered.
- Particles are collision less.
Q.2.9 Find the Lorentz force in static and uniform magnetic field?
Answer: We know that for static and uniform magnetic field (E= 0) and B = uniform. Then Lorentz force
$$F=q\left(E+\left(\overline{V}\times\overline{B}\right)\right)$$
∵ E = 0
$$F=q\ \left(0+\left(\overline{V}\times\overline{B}\right)\right)$$
$$\because F=ma$$
$$\because a=\ \frac{dv}{dt}$$
$$F=m\frac{dv}{\ dt}$$
So,
$$F=q(V\times B)$$
$$m\frac{dV}{dt}=q\left(V\times B\right)$$
This gives information about motion of particle.
Q.2.10 Write down the reasons of spiral path of ions and electrons?
Answer: Ions and electrons have spiral path. Ion spiral in which spring path or gap is more.
Reasons:
- In first half particle gain energy move linearity and $V⟂ ,rL$ increases.
- 3-D orbit in space has slanted helix with changing path.
- In $2^{nd}$ half particle losses energy and $r_L$ decreases.
