A beam of cathode rays is subjected to crossed electric (E) and m… - Vidyadip

MCQ

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 $V$ potential diffrence between kethod and anode)

A
$\frac{{{B^2}}}{{2V{E^2}}}$
B
$\;\frac{{2V{B^2}}}{{{E^2}}}$
C
$\;\frac{{2V{E^2}}}{{{B^2}}}$
✓
$\frac{{{E^2}}}{{2V{B^2}}}$

✓

Answer

Correct option: D.

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

d
When a beam of cathode rays (or electrons) are subjected to crossed electric $(E)$ and magnetic $(B)$ fields, the beam is not deflected, if Force on electron due to $=$ Force on electron due magnetic field to electric field

$Be\upsilon = eE$

or $\quad v=\frac{E}{B}$ ...... $(i)$

If $V$ is the potential difference between the anode and the cathode, then

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

${\frac{e}{m}=\frac{v^{2}}{2 V}}$ ..... $(ii)$

Substituting the value of $v$ from equation $(i)$ in equation $(ii)$, we get

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

Specific charge of the cathode rays $\frac{e}{m}=\frac{E^{2}}{2 V B^{2}}$

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