An electron moves around the nucleus in a hydrogen of radius `0*51 Å` with a velocity of `2xx10^6m//s`. Calculate (i) the equivalent current due to orbital motion, (ii) magnetic field produced at the centre of nucleus. (iii) magnetic moment associated with electron.

Explanation

Equivalent current due to the orbital motion of electron is given by:
`I = e/T = (ev)/(2pi v)`
here ` e = 1.6 xx 10^(-19) C, v = 3 xx 10^6 m//s`
`r = 0.51 Å = 0.51 xx 10^(-10) m`
` rArr I = (1.6 xx 10^(-19) xx 3 xx 10^6)/(2 xx 3.14 xx 0.51 xx 10^(-10))`
` = 1.5 xx 10^(-3) A`
Magnetic moment associated with the electron is
M=IA
`= 1.5 xx 10^(-3) xx 3.14 xx (0.51 xx 10^(-10))^2`
` = 12.25 xx 10^(-24) Am^2`