Answer to Question #298317 in Electricity and Magnetism for Ase

Question

An electron penetrates the region between two uniformly charged horizontal plates, but oppositely signed. Its initial speed, at half distance between the plates is 2×10 ^6 i m/s. The plates have a length of 4 cm and are 1.6 cm apart. In the whole region between the plates, the electric field ́ is uniform and perpendicular to the plates. (a) what is the maximum modulus that the vertical electric field can have so that the electron does not touch any plate?

The answer is 228 N/C but I'm not too sure how they got that?

Answer 1

Velocity

$v=2\times10^6\hat{i}m/sec$

L=4cm

b=1.6cm

Time

$t=\frac{s}{v}$

$t=\frac{0.04}{2\times10^6}=2\times10^{-8}sec$

$s=ut+\frac{1}{2}at^2$

$0.005=0+0.5\times a\times4\times10^{-16}$

$$a=\frac{0.005}{0.5\times4\times10^{-16}}=2.5\times10^{13}m/sec^2$$

$a=\frac{eE}{m}$

$E=\frac{ma}{e}$

Put value

$$E=\frac{9.1\times10^{-31}\times2.5\times10^{13}}{1.6\times10^{-19}}=228N/C$$