Electron of mass m and charge q is travelling with a speed v along a circular path of radius at right angles to a uniform magnetic field of intensity B. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius

Options

A. `2r`
B. `4r`
C. `r//4`
D. `r//2`

Answer

b

Explanation

In circular path, centripetal force of electron is equal to the force due to magnetic field. : `:.(mv^(2))/(r)=qnuBsin90^(@)impliesr=(mnu)/(qB)`
If the speed of the electron is doubled and the magnetic field is halved.
Then.`r.=(m2nu)/(q(B//2))=2xx2xx(mnu)/(qB)=4r`