Question

The parallel plate capacitor has potential difference of $100 \, V$ and separation between the plate is $1 \, mm$ . 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)

$F_{e l e c t r i c}=F_{m a gnetic}$
$eE=e\left(V \times B\right)$
$B=E/V=\left(\frac{Potential difference}{distance}\right)\frac{1}{speed}=\frac{100}{1 \times 1 0^{- 3} \times 1 0^{5}}$
$=1T$
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.