Question

When the velocity of a relativistic charged particle increases, its specific charge ______.

Answer 1

Relativistic charged particle:

For a relativistic particle, the relativistic mass is given by,

$\mathrm{m}=\frac{{\mathrm{m}}_{\mathrm{o}}}{\sqrt{1-{\displaystyle \frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}}}.....\left(1\right)$

Here,

$m$ is the relativistic mass

$m_0$ is the rest mass

$v$ is the velocity of the particle

$c$ is the speed of light

Now the specific charge is the charge per mass.

Mathematically,

Specific charge $=\frac{\mathrm{q}}{\mathrm{m}}.....\left(2\right)$

Now putting equation 1 in 2 we get,

$\frac{\mathrm{q}}{\mathrm{m}}=\frac{\mathrm{q}}{{\mathrm{m}}_0}\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}.....\left(3\right)$

From equation $3$ we can see that a specific charge is inversely proportional to the velocity of the particle.

Hence, increasing particle velocity leads to decrease in specific charge.