Question

The parallel plate capacitor has potential difference of $100V$ and separation between the plate is $1mm$ . An electron is projected along $x$ axis in between the plates. If the electron comes out of the plates along the $x$ axis undeviated then the magnitude and direction of magnetic field that must be applied between the plates : (particle is projected with a velocity of $10^{5}m/s$ along $x$ axis)

• A. $B=1\hat{k}T$
• B. $B=1\hat{j}T$
• C. $B=1\left(-\hat{j}\right)T$
• D. $B=10\left(-\hat{j}\right)T$

Answer 1

Answer: (B)

$F_{electric}=F_{magnetic}$
$eE=e\left(V\times B\right)$
$B=E/V=\left(\frac{Potentialdifference}{distance}\right)\frac{1}{speed}=\frac{100}{1\times 10^{-3}\times 10^5}$
$=1T$
Electric force is along $\left(+\hat{k}\right)$ direction then magnetic force must be in $-\hat{k}$ direction.
Therefore, $B$ must be in $+\hat{j}$ direction.