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Electron is rotating in circular orbit w...

Electron is rotating in circular orbit with radius `5.2xx10^(-11)m` and with linear speed `2xx10^(6)ms^(-1)` in an hydrogen atom around the proton. Find the magnetic field produced at the centre of the orbit.

Text Solution

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1. `v=2xx10^(6)ms^(-1),r=5.2xx10^(-11)m`
`e=1.6xx10^(-19)C`
2. Frequency of electron in the orbit f (No. of rotations completed in 1 second) f = `v/(2pir)`
3. Electric current I = f.e
= `v/(2pir)xxe`
= `(2xx10^(6))/(2xx3.14xx5.2xx10^(-11))xx1.6xx10^(-19)`
= `9.8xx10^(-4)A`
4. Magnetic field produced at the centre of the circular orbit,
`B=(mu_(0)I)/(2r)`
`thereforeB=(4xx3.14xx10^(-7)xx9.8xx10^(-4))/(2xx5.2xx10^(-11))`
`thereforeB=11.8T`
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