A beam of cathode rays is subjected to crossed Electric (E) and magnetic field (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)

B²/2VE²

2VB²/E²

2VE²/B²

2E²/2VB²

Solution

2E²/2VB²

As the electron beam is not deflected,
then
F_m = F_e
Or BeV = Ee
Or v= E/B .... (i)
As the electron moves from the cathode to anode, its potential energy at the cathode appears as its kinetic energy at the anode. If V is the potential difference between the anode and cathode, then potential energy of the electron at cathode = eV. Also, the kinetic energy of the electron at anode = mv² /2. According to law of conservation of energy
$1 half space mv squared space equals space eV or space straight v equals space square root of fraction numerator 2 eV over denominator straight m end fraction end root space space space... space left parenthesis ii right parenthesis From space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space have square root of fraction numerator 2 eV over denominator straight m end fraction end root space equals space straight E over straight B Or space straight e over straight m space equals space fraction numerator straight E squared over denominator 2 VB squared end fraction$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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