An electron is projected into a uniform electric field of strength 2000 newton per coulomb with initial velocity 10 to the power 6 m per second perpendicular to the field how much electron is deflected after it has travelled 1 cm
Answers
Given: An electron is projected in electric field of strength 2000 N/C, it has initial velocity 10^6 m/s .
To find: How much electron is deflected after it has travelled 1 cm?
Solution:
- Now, distance covered by electron is = 1 cm or 0.01 m
- Then, time taken will be:
distance covered/speed of electron
= 0.01 / 10^6
= 10^-8 sec
- Let the deflection due to force be x from is position.
- The acceleration of electron due to electric field is:
a = q x E / m
where q is charge on electron, that is q = 1.6× 10^-19 C
E is electric field, that is E = 2000 N/C
m is mass of electron, that is m = 9.1 x 10^-31 Kg
- Putting these values in acceleration, we get:
a = 1.6 x 10^-19 x 2000 / 9.1 x 10^-31
= (3200/9.1) x 10^12 m/s²
= 3.516 x 10^14 m/s²
- Now, deflection of electron will be:
x = 1/2at^2
x = 1/2 x 3.516 x 10^14 x (10^-8)^2
x = 1/2 x 3.516 x 10^14 x 10^-16 m
x = 1.758 x 10^-2 m
Answer:
Electron is deflected by 1.758 x 10^-2 m after it has travelled 1 cm.