Speed of an electron in an electric field - trying to find my error.

In summary, the speed of an electron in an electric field can be calculated using the formula v = E/m, where v is the speed, E is the electric field strength, and m is the mass of the electron. The speed of the electron in an electric field depends on the strength of the electric field, with a higher electric field resulting in a higher speed. The units typically used to measure the speed of an electron in an electric field are meters per second (m/s). The speed of an electron in an electric field cannot exceed the speed of light, as stated by the theory of relativity. To determine the correctness of a calculation for the speed of an electron in an electric field, one can compare it to the accepted value of
  • #1
rowkem
51
0

Homework Statement



Two stationary positive point charges, charge 1 of magnitude 3.45 nC and charge 2 of magnitude 1.85 nC, are separated by a distance of 50.0 cm. 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 v(final) of the electron when it is 10.0 cm from charge 1?

Homework Equations



Ek= (mv^2)/2
U= (k(q1q2))/r

The Attempt at a Solution



I used the following equation:

Ek(f)+U(f) = Ek(i)+U(i)

(mv(f)^2)/2 + (k(q1q2))/r = (mv(i)^2)/2 + (k(q1q2))/r

(9.1x10^-31)(vf)^2)/2 + (((9x10^9)(3.45nC)(1.6x10^-19))/0.10m) + (9x10^9)(1.85nC)(1.6x10^-19))/0.40m) = (((9x10^9)(3.45nC)(1.6x10^-19))/0.25m) + (9x10^9)(1.85nC)(1.6x10^-19))/0.25m)

(9.1x10^-31)(vf)^2)/2 + 5.6x10^-17 = 3.0 x 10^-17

(9.1x10^-31)(vf)^2)/2 = -2.6 x 10^-17

Then my issue: I end up needing to take the square root of a negative number...yah.

If someone could please point me to the error I've made, it would be appreciated. I'm iffy on my "Ek(f)+U(f) = Ek(i)+U(i)". Did I use the correct equations? Please help, thanks.
 
Physics news on Phys.org
  • #2
You are releasing an electron which carries a negative charge. It looks like you haven't carried that into the calculation of U correctly.
 
  • #3
That would do it. I end up getting 7.53x10^6 m/s. Seems high - thoughts before I submit?
 
  • #4
rowkem said:
That would do it. I end up getting 7.53x10^6 m/s. Seems high - thoughts before I submit?

I didn't follow your calculation, but off the cuff with mass at 10-31 a little change in potential should go a long way.
 

1. What is the formula for calculating the speed of an electron in an electric field?

The formula for calculating the speed of an electron in an electric field is v = E/m, where v is the speed, E is the electric field strength, and m is the mass of the electron.

2. How does the speed of an electron change in an electric field?

The speed of an electron in an electric field depends on the strength of the electric field. As the electric field strength increases, the speed of the electron also increases.

3. What units are used to measure the speed of an electron in an electric field?

The speed of an electron in an electric field is typically measured in meters per second (m/s).

4. Can the speed of an electron in an electric field be greater than the speed of light?

No, according to the theory of relativity, the speed of light is the maximum speed at which any object can travel. Therefore, the speed of an electron in an electric field cannot exceed the speed of light.

5. How can I determine if my calculation for the speed of an electron in an electric field is correct?

You can check your calculation by comparing it to the accepted value for the speed of an electron in an electric field, which is approximately 2.2 x 10^6 m/s. You can also double-check your equations and ensure that all units are consistent.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
13K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
Back
Top