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CBSE Class 12-science Answered

A charge Q mass M moving around a fixed charge q in a circular path radius r.then what's the time period (T) of charge Q?
Asked by tapas.purna | 12 Oct, 2019, 11:39: PM
answered-by-expert Expert Answer
if a charge Q of mass M is moving around a fixed charge in circular path, electrostatic force is utilized as centripetal force.
 
Hence begin mathsize 14px style fraction numerator Q space q over denominator 4 pi epsilon subscript o space R squared end fraction space equals space fraction numerator M space v squared over denominator R end fraction space space o r space space space v space equals space open parentheses fraction numerator Q space q over denominator 4 pi epsilon subscript o R space M end fraction close parentheses to the power of 1 divided by 2 end exponent end style..........................(1)
where v is speed of charge Q in the circular path, R is radius of circular path and εo is the permittivity of free space .
 
If T is time period of circular orbit, then we have,  v = (2πR)/T   .....................(2)
 
By equating (1) and (2), we get
 
begin mathsize 14px style T space equals space 4 space pi to the power of bevelled 3 over 2 end exponent space R to the power of bevelled 3 over 2 end exponent space open parentheses fraction numerator epsilon subscript o M over denominator Q space q end fraction close parentheses to the power of bevelled 1 half end exponent end style
Answered by Thiyagarajan K | 13 Oct, 2019, 08:29: AM

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