Electron revolving with speed v is producing magnetic field B at center. Find relation between radius of path B and v?

Options

A. `B propto v propto 1/r`
B. `B propto v propto 1/r^(2)`
C. `B propto v^(2) propto 1/r`
D. `B propto v^(2) propto 1/r^(2)`

Answer

B

Explanation

`therefore` Magnetic field at center.
`B=(mu_(0)I)/(2r)`
Where, `I=e/t`
or `i= e/((2pir)/v) = (ev)/(2pir)`
Hence, `B=(mu_(0))/(2r)((ev)/(2pir)) = (mu_(0)ev)/(4pir^(2))`
or `B propto v/I^(2)`