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  • (b) Is the formula you employ in (a) valid for calculating radius of the path of a 20 MeV electron beam? If not, in what way is it modified?

Q: 11.21 (b) Is the formula you employ in (a) valid for calculating radius of the path of a 20\hspace{1mm}MeV electron beam? If not, in what way is it modified? 

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The formula used in (a) can not be used. As the electron would be travelling at a very high speed we can not take its mass to be equal to its rest mass as its motion won't be within the non-relativistic limits.

The value for the mass of the electron would get modified to

m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

where m is the relativistic mass, m0 is the rest mass of the body, v is the very high speed at which the body is travelling and c is the speed of light.

The radius of the circular path would be

r=\frac{m_{e}v}{eB\sqrt{1-\frac{v^{2}}{c^{2}}}}

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Sayak

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