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Let us consider an elctron having an intial velocity of ‘v’ m/s along the tube excess ‘OP’ at point ‘

Let us consider an elctron having an intial velocity of ‘v’ m/s along the tube excess ‘OP’ at point ‘?’ and assume that there is a uniform magnetic field of flux density ‘B’ (wb/m2) covering an axis distance ‘l’.

The force acting on the electron, entering the field is
F=qBv
This force is in the direction perpendicular to the path which is an arc of radius ‘R’ given by,
R=mv/qB
The electron emerges from the field and moves in the direction inclined at an angle ‘?’ to the axis and strike the screen at ‘P’.
If the total angular deflection is very small then,
OM=l
And angular deflection ‘?’ is equal to
‘?’=l/R
=lqB/mv
D= Ltan?=tan?
Therefore
D=LlqB/mv
Substituting ‘v’ equals to
v

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