A beam of cathode rays is subjected to crossed electric (E) and magnetic fields . The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by

Question

A beam of cathode rays is subjected to crossed electric (E) and magnetic fields . The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by (A)  (B2/2VE2)  (B)  (2VB2/E2)  (C)  (2VE2/B2)  (D)  (E2/2VB2)

Tardigrade Admin · Accepted Answer

As the electron beam is not deflected, then

F_{m} = F_{e}

or

B e v = E e

or

v = \frac{E}{B}

... (i) As the electron moves from 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, kinetic energy of the electron at anode

= \frac{1}{2} m v^{2} .

According to law of conservation of energy

\frac{1}{2} m v^{2} = e V

or

v = \frac{2 e V}{m}

?(ii) From Eqs. (i) and (ii), we have

\frac{2 e V}{m} = \frac{E}{B}

or

\frac{e}{m} = \frac{E ^{2}}{2 V B ^{2}}

Note : - (where V is the potential difference between cathode and anode)

Q. A beam of cathode rays is subjected to crossed electric (E) and magnetic fields . The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by

$\frac{B ^{2}}{2 V E ^{2}}$

$\frac{2 V B ^{2}}{E ^{2}}$

$\frac{2 V E ^{2}}{B ^{2}}$

$\frac{E ^{2}}{2 V B ^{2}}$

Q. A beam of cathode rays is subjected to crossed electric (E) and magnetic fields . The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by

2VE2B2​

E22VB2​

B22VE2​

2VB2E2​

$\frac{B ^{2}}{2 V E ^{2}}$

$\frac{2 V B ^{2}}{E ^{2}}$

$\frac{2 V E ^{2}}{B ^{2}}$

$\frac{E ^{2}}{2 V B ^{2}}$