An electron of charge e moves in a circular orbit of radius r around a nucleus. The magnetic field due to orbital motion of the electron at the site of the nucleus is B. The angular velocity ω of the electron is

Question

An electron of charge e moves in a circular orbit of radius r around a nucleus. The magnetic field due to orbital motion of the electron at the site of the nucleus is B. The angular velocity ω of the electron is

Infinity Learn · Accepted Answer

The electron moving in a circular orbit is equivalent to a current carrying loop. If v be its frequency, $$theni=ve=e/T$$ (T=$$ time period $$)We$$ know that $$T=(2$$$$π$$$$r/v)∴ $$i=ev2$$$$π$$$$r=e(r$$ω$$)2$$$$π$$$$r=e$$ω$$2$$π                    $$(where$$ ω $$=$$ angular $$frequency)The$$ magnetic field at the centre of the $$loopB=$$μ$$0i2ror$$ $$B=$$μ$$02re$$ω$$2$$π$$=$$μ$$0e$$ω$$4$$$$π$$r∴           ω$$=4$$$$π$$rBμ$$0e$$

An electron of charge e moves in a circular orbit of radius r around a nucleus. The magnetic field due to orbital motion of the electron at the site of the nucleus is B. The angular velocity $ω$ of the electron is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material