Question

speed on an electron

Two stationary positive point charges, charge 1 of magnitude 3.25nC and charge 2 of magnitude 1.75nC , are separated by a distance of 42.0cm . An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

What is the speed vfinal of the electron when it is 10.0cm from charge 1?

Express your answer in meters per second.

Answer 1

In order to calculate the speed of the elctron first of all we calculate the net force on the electron due to the presence of two static charges. Secondly, we find the acceleration experienced by the electron due to this force. Thirdly, by using the equations of motion for a linear motion we calculate the final speed.

1) The electrostatic force between the two charges q₁ and q₂ can be calculated by using Colimb's Law

where r is the separation between the charges.

The force F₁ acting on electron having charge -1.6 X 10^-19 C due to the presence of another charge 1.75 nC (1.75 X 10^-9 C) can be calculated by using the above formula. Since the electron is intially placed at the mid away of the line joining the two charged particles so the separtion comes out to be 42 cm / 2 =21 cm=0.21 m.

Since the charges have opposite signs so the nature of the force will be attractive and will be directed towards the charge of 175nC.

The force F₂ experienced by the electron due to 3.25 nC (3.25 X 10^-9 C) charge is

Direction of this force is towards the 3.25nC charge.

The two forces F₁ and F₂ are directed in opposite directions and the force is a vector quantity so the net force Facting on electron is given as

F = F₂ - F₁ = (1.06 - 0.57) X 10^-16 N = 0.49 X 10^-16 N

As F₂ is of higher in magnitude than F₁ so F will be directed towards 3.25nC charge.

2) The acceleration a of electron having mass m (9.1 X 10^-31 kg) due to 0.49 X 10^-16 N force can be calculated as

a = F/m =( 0.49 X 10^-16 N) / (9.1 X 10^-31 kg) = 5.38 X 10¹³ m/s^2.

3) TO find the final speed v of electron we use

Initially electron was at rest so intial speed u=0.

and the displacement s = (21 -10 )cm =11 cm =0.11 m

The final speed of electron is 3.44 X 10⁶ m/s.