A beam of cathode rays is subjected to crossed electric (E) and magnetic (B) fields. 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)

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

B $\frac{B^2}{2VE^2}$

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

D $\frac{2VE^2}{B^2}$

The answer is A.

Solution

The beam is undeflected when the electric and magnetic forces balance: $eE = evB$, so $v = \frac{E}{B}$
The electrons gain their speed from the accelerating potential V: $eV = \frac{1}{2}mv^2$
$\frac{e}{m} = \frac{v^2}{2V}$
Substituting $v = \frac{E}{B}$: $\frac{e}{m} = \frac{E^2}{2VB^2}$

Concept Velocity selector and specific charge

Motion in Combined Electric and Magnetic Fields in past papers

13 questions from this chapter have appeared across 10 exam years.

A beam of cathode rays is subjected to crossed electric (E) and magnetic (B) fields. 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)

Solution

Motion in Combined Electric and Magnetic Fields in past papers

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