Two spherical objects are separated by a distance of 2.41 x 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 4.18 x 10-21 N. How many electrons did it take to produce the charge on one of the objects?

This is the work that I did....

I first found that Q= 1.64 x 10 ^ -18.

I then divided by e.

The answer I got was 10.23, but I am being told that is wrong.

who told you it was the wrong answer?

I submitted it online and I was told it was wrong. I also tried 10.22 and 10.24 to see if there was a rounding error.

I just realized that the answer had to be 10. Im sorry for any confusion. Thank you for your help though.

To find the number of electrons needed to produce a certain charge, you need to use the elementary charge (e) and the charge formula Q = ne, where Q is the total charge, n is the number of electrons, and e is the elementary charge.

In your case, since both objects acquire the same negative charge, each object will have a charge of Q/2.

Using the given magnitude of the electrostatic force (F) and the distance (r) between the objects, you can use Coulomb's law to find the charge (Q) on one of the objects:

F = k * (Q/2)^2 / r^2

where k is the electrostatic constant.

Plugging in the values, you can solve for Q.

Now, you can use the charge formula to find the number of electrons (n) needed to produce that charge:

n = Q / e

Substituting the value of Q you found into this formula will give you the answer.

Let's do the calculations:

Given:
F = 4.18 x 10^-21 N
r = 2.41 x 10^-3 m

Using Coulomb's law:
k = 8.99 x 10^9 N⋅m^2/C^2

F = k * (Q/2)^2 / r^2
4.18 x 10^-21 N = (8.99 x 10^9 N⋅m^2/C^2) * (Q/2)^2 / (2.41 x 10^-3 m)^2

Now calculate Q:

Q = sqrt((4.18 x 10^-21 N) * (2.41 x 10^-3 m)^2 / (8.99 x 10^9 N⋅m^2/C^2)) * 2

After evaluating Q, you can then calculate the number of electrons (n):

n = Q / e

Substituting the value of Q into this formula will give you the final answer.

Make sure to follow the proper order of operations and use the correct units while performing the calculations.