Question

Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference `V` along `X`-axis.These electrons emerges from a narrow hole into a unifrom magnetic field `B` directed along the axis.However, some of the electrons emerging from the hole make slightly divergent angles as shown in figure.These paraxial electrons meet for second time on the `X`-axis at a distance `sqrt((Npi^(2)mV)/(eB^(2)))`.Then find value of `N`.(Neglect interaction between electrons)

Answer 1

Correct Answer - B::C
Pitch `=(2pimcostheta)/(qB) eV=1/2mv^(2)`
`=(2pisqrt(2meV))/(eB) (costheta~~1) rArr "pitch" =sqrt((8pi^(2)mV)/(eB^(2)))`
`:.` Distance from point of divergence `=sqrt((32pi^(2)mV)/(eB^(2)))`