Question

An electron accelerated through a potential difference $V$ passes through a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$, the electron in the same magnetic field will experience a force :

• A. $F$
• B. $F/2$
• C. $\sqrt{2}F$
• D. $2F$

Answer 1

Answer: (C)

$\sqrt{2}F$

force is given as:

$F=Bqv$

The kinetic energy of an electron after passing through a potential difference of V volt is given as

But $\frac{1}{2}m{v}^2=eV$ or

$V=\sqrt{\frac{2eV}{m}}$

$F=Bq\sqrt{\frac{2eV}{m}}\Rightarrow F\propto \sqrt{V};F^{\prime }\propto \sqrt{2V};$

$\frac{F^{\prime }}{F}=\sqrt{2}or{F}^{\prime }=\sqrt{2}F$