An electron (mass `9xx10^(-31)kg`, charge `1.6xx10^(-19C)` moving with a velocity of `5xx10^(6)m//s` enters a region where a magnetic field exists. The magnetic field is in a direction perpendicular to the initial velocity of the electron. If the electron describes a circle of radius 0.1 m, the intensity of the magnetic field must be `etaxx10^(-4)T`. Then `eta` is __________.

Answer

8.87

Explanation

Since angle between velocity vector and magnetic field direction `theta` is in between `0^(@)` and `90^(@)` so the path of electron will be helical and electrons will focus again on distances equal to integral multiplication of pitch distances.
Required minimum distance `x=`Pitch
`=v cos theta xxT=v cos theta xx (2pim)/(qB)=sqrt((2E)/m)xxcos thetaxx(2pim)/(qB)=2sqrt(2)pi cos theta xx(sqrt(mE))/(qB)[:' theta` is small `:.cos theta ~~1]`