Question

At some instant the velocity components of an electron moving between two charged parallel plates are

vx=2.5×105m/s
and
vy=5.0×103m/s
. Suppose the electric field between the plates is uniform and given by
E⃗ =(120N/C)j^
. In unit-vector notation, what are (a) the electron's acceleration in that field and (b) the electron's velocity when its x coordinate has changed by 2.0 cm?

Answer 1

Step-by-step explanation:

the electric field between the plates is uniform and given by

E⃗ =(120N/C) j

So electric field is along y - axis

Force on electron

F_y = 1.6 x 10⁻¹⁹ x 120

a_y ( acceleration )= ( 1.6 x 10⁻¹⁹ / 9.1 x 10⁻³¹ ) x 120

a_y = 21.1 x 10¹²

a = 21.1 x 10¹² j

time to reach x = 2 cm = 2 x 10⁻² m

t = 2 x 10⁻² / 2.5 x 10⁵

= .8 x 10⁻⁷

= 8 x 10⁻⁸ s

velocity along y axis after time 8 x 10⁻⁸ s

= u + at

= 5 x 10³ + 21.1 x 10¹² x 8 x 10⁻⁸

= 5 x 10³+ 168.8 x 10⁴

= .05 x 10⁵ + 16.88 x 10⁵

= 16.93 x 10⁵

resultant velocity

= √( 2.5 x 10⁵ )² + ( 16.93 x 10⁵)²

= 17.11 x 10⁵ m /s