Question

Find specific charge if an cathode ray is passed through cross feilds in terms of (E) (B) and (V).Where E is electric feild, B is magnetic feild and V 8s pot. differene

Answer 1

As per the given question,

Let the charge of the cathode beam is Q, mass of the charge is m, it is passing in the magnetic field B and electric field E, in the potential difference V. let the radius of the cathode ray is R,

Now, applying the conservation of energy,

$QV=\dfrac{mv^2}{2}------(i)$

Now,

$\Rightarrow QvB=QE$

$\Rightarrow v=\dfrac{E}{B}------(ii)$

now substituting the value of v in equation (i) from equation (ii)

$QV=\dfrac{mE^2}{2B^2}$

$\Rightarrow \dfrac{Q}{m}=\dfrac{E^2}{2B^2V}$