A beam of cathode rays is subjected to crosse | vedclass

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(D) When a beam of cathode rays (electrons) is subjected to crossed electric $(E)$ and magnetic $(B)$ fields,the beam is not deflected if the force du

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$\frac{E^2}{2VB^2}$

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(D) When a beam of cathode rays (electrons) is subjected to crossed electric $(E)$ and magnetic $(B)$ fields,the beam is not deflected if the force due to the electric field equals the force due to the magnetic field.$Be v = eE$$v = \frac{E}{B}$ ..... $(i)$If $V$ is the potential difference between the anode and the cathode,the kinetic energy gained by the electron is given by:$\frac{1}{2} m v^2 = eV$$\frac{e}{m} = \frac{v^2}{2V}$ ..... $(ii)$Substituting the value of $v$ from equation $(i)$ into equation $(ii)$,we get:$\frac{e}{m} = \frac{(E/B)^2}{2V} = \frac{E^2}{2VB^2}$Thus,the specific charge of the cathode rays is $\frac{E^2}{2VB^2}$.

$A$ beam of cathode rays is subjected to crossed electric $(E)$ and magnetic fields $(B).$ The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by (where $V$ is the potential difference between cathode and anode):

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