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)

Electrons emitted with negligible speed from an electron gun are accel

1.	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» SOLUTION :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)))`

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