Question

two proton enter a region of transverse magnetic field what will be ratio of time period of revolution if the ratio of energy is 2root2:root3
and is 1:1
explain in detail solution

Answer 1

Answer:

wo proton enter a region of transverse magnetic field what will be ratio of time period of revolution if the ratio of energy is 2root2:root3. and is 1:1

Explanation:

Answer 2

Given:

Two protons in same magnetic field. so mass and charge both particles is same.

The ration of their energies is:

$\frac{E_1}{E_2} = \frac{2\sqrt 2}{\sqrt 3}$

To find: The ratio of time period of revolutions i.e. $\frac{T_1}{T_2}$

Formula Used:

The period is given by:

$T=2\pi \sqrt{\frac{mr}{qvB}}$

Energy of particle is

$E=\frac{1}{2}mv^2$

Calculation:

The radius also depends on energy but when we will substitute it, the period will be related to energy as follows:

$T\propto \frac{1}{v}\\v\propto \sqrt E\\\Rightarrow T\propto \frac{1}{\sqrt E}\\\frac{T_1}{T_2}=\sqrt \frac{E_2}{E_1}\\\frac{T_1}{T_2}=\sqrt \frac{\sqrt 3}{2\sqrt 2}\\\frac{T_1}{T_2}= (\frac{3}{8})^{\frac{1}{4}}$

Learn more about: charged particles in magnetic field.

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