The electron in a H-atom circles around the proton with a speed of `2.18 xx 10^(6) ms^(-1)` in an orbit of radius `5.3 xx 10^(-11)` um.
Calculate
(i) the equivalent current
(ii) magnetic field produced at the proton.
Given, charge on electron is `1.6 xx 10^(-19)` C and `mu_(0) = 4pi xx 10^(-7) T mA^(-1)`

Explanation

Here, `v = 2.18 xx 10^(6) m//s, r = 5.3 xx 10^(-11) m`
`e = 1.6 xx 10^(-19)` C
(i) Time period of revolution of electron is given by:
`T = (2pir)/v = (2pi xx 5.3 xx 10^(-11))/(2.18 xx 10^(6)) = 1.528 xx 10^(-16) s`
Equivalent current,
`I = ("Charge")/("Time") = e/T`
`rArr I = 1.05 xx 10^(-3) A`
(ii) Field at proton due to orbiting electron is:
`B = (mu_(0)I)/(2r)` or `B = mu_(0)/(4pi). (2piI)/r`
`B = (10^(-7) xx 2pi xx 1.05 xx 10^(-3))/(5.3 xx 10^(-11)) = 12.4 T`