An electron and a proton have charges of equal magnitude but of opposite sign. The magnitude of the charge is 1.6 x 10-19 C. If the electron and proton in are separated by a distance of 5 x 10-11 m, what is the magnitude of the electrostatic force exerted on the electron by the proton?
Give your answer in nano Newtons. ( Divide your answer by 10-9)
Hello, I would like to know how to do this, do I use the F=kq1q2/ r^2? And would it look something like this?
F= 9 x 10^9 (1.6 x 10^-19)(1.6 x 10^-19)/ 5^2 because this is what I did and got 9.2 x 10^-29, but when I plugged it in I got it wrong. How to I do this problem and place it in nano Newtons, do I divide F= 9 x 10^9 (1.6 x 10^-19)(1.6 x 10^-19) by 10^2? I got 2.3 x 10^-29. Please tell me what I'm doing wrong.
the distance is not 5m
(9 * 10^9)(1.6 * 10^-19)(-1.6 * 10^-19) / (5 * 10^-11)^2
= -9.216 * 10^-8
= -92.16 nJ
You are correct in using the formula F = k * q1 * q2 / r^2, where F represents the electrostatic force between two charged particles, k is the electrostatic constant (approximately 9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between the particles.
To solve this problem, substitute the given values into the formula. The magnitude of the charge of both the electron and proton is 1.6 x 10^-19 C. The distance between them is 5 x 10^-11 m. Plugging in these values, the equation becomes:
F = (9 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5 x 10^-11 m)^2
Evaluating this expression, you should get F = 2.304 x 10^-29 N. Now, to convert this value to nano Newtons (nN), you divide by 10^-9:
F = (2.304 x 10^-29 N) / (10^-9)
Simplifying further, the answer is F = 2.304 x 10^-20 nN.
So, the correct magnitude of the electrostatic force exerted on the electron by the proton is 2.304 x 10^-20 nN.
To find the magnitude of the electrostatic force exerted on the electron by the proton, you're correct in using the formula F = k * q1 * q2 / r^2, where F is the force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's calculate it step-by-step:
1. Plug in the values:
q1 = 1.6 x 10^-19 C (charge of the electron)
q2 = 1.6 x 10^-19 C (charge of the proton)
r = 5 x 10^-11 m (distance between the charges)
k = 9 x 10^9 Nm^2/C^2 (electrostatic constant)
2. Substitute the values into the formula:
F = (9 x 10^9 Nm^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5 x 10^-11 m)^2
3. Simplify the equation:
F = 230.4 x 10^-38 / 25 x 10^-22
F = (230.4 / 25) x (10^-38 / 10^-22)
F = 9.216 x 10^-38-(-22)
F = 9.216 x 10^-16 N
4. To convert the answer to nano Newtons, divide it by 10^9:
F = (9.216 x 10^-16) / (10^9)
F = 9.216 x 10^-25 N
So, the magnitude of the electrostatic force exerted on the electron by the proton is 9.216 x 10^-25 N, which is equivalent to 0.009216 nano Newtons.