Question

In Bainbridge mass - spectrometer a potential difference of $1000\text{V}$ is applied between two plates placed $1\text{cm}$ apart and there exist a magnetic field of $B=1\text{T}$. The velocity of undeflected positive ions from the velocity selector is

• A. ${10}^7{\text{ms}}^{-1}$
• B. ${10}^4{\text{ms}}^{-1}$
• C. ${10}^5{\text{ms}}^{-1}$
• D. ${10}^2{\text{ms}}^{-1}$

Answer 1

The correct option is C ${10}^5{\text{ms}}^{-1}$

Given,
$V=1000\text{V}d=1\text{cm}=1\times {10}^{-2}mB=1\text{T}$

$\because E=\frac{V}{d}=\frac{1000}{1\times {10}^{-2}}={10}^5{\text{Vm}}^{-1}$

Condition for the undeviated motion of positives ions is,

Electric force = magnetic force

$\Rightarrow qE=qvB$

$v=\frac{E}{B}=\frac{{10}^5}{1}={10}^5{\text{ms}}^{-1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.