Question

There's an electric field in some region of space that doesn't change with position.

An electron starts moving with a speed of 2.0 ×× 1077 m/sm/s in a direction opposite to the field.

Its speed increases to 4.0 ×× 1077 m/sm/s over a distance of 1.6 cmcm.

Answer 1

Let the magnitude of electric field strength be E

We have to calculate E

Given

Initial speed of electron(v_i) = 2.0 x 10⁷ m/s

Final speed of electron(v_f) = 4.0 x 10⁷ m/s

distance travelled by electron (s) = 1.6 cm = 1.6 x 10^-2 m

Charge on electron (e) = 1.6 x 10^-19C.

Since electron is moving opposite to electric field

Electric force acting on electron (F_e) = e. E

Mass of electron(m) = 9.1 x 10^-31 kg

Acceleration of electron

Using third equation of motion

  v_f² - v_i² = 2 a.s

Putting values

(4 x 10⁷)² - (2 x 10⁷)² = 2 a . (1.6 x 10^-2)

12 x 10¹⁴ = a . (3.2 x 10^-2)

SO a = 3.75 x 10¹⁶ m/s²  

  Also   

So a = 3.75 x 10¹⁶ = [(1.6 x 10^-19) x ( E) ] / (9.1 x 10^-31)

3.75 x 10¹⁶ = 1.758 x 10¹¹ x E

E = 2.13 x 10⁵ N/C

Hope the explanation would be helpful for you.