Finding the electric force on each sphere

[rela]

Dear experts,

Please guide me along with this problem.

Two identical small conducting spheres are separated by 0.60 m. The spheres carry
different amounts of charge and each sphere experiences an attractive electric force of
10.8 N. The total charge on the two spheres is −24 μC. The two spheres are connected
by a slender conducting wire, which is then removed. The electric force on each sphere is
closest to:

I attempted on it by finding the charges on each sphere to be (-60uC & +36uC) and initially i thought the answer was 0N since the conducting wire will conduct away all the negative charges from one sphere to the positively charged sphere, thus the negatively charged sphere becomes neutral eventually.

However, as I thought longer, it doesn't seem so. Can someone pls explain to me what exactly happans and enlighten me on the exact interaction between the charges from moment to moment before arriving to the final answer?

Thanks for the help!

Regards
Rela

 

[michalll]

The answer is really simple, after connecting, since their identical the charge will distribute on both spheres the same, thus each sphere will bear -12 uC.

 

[Moetasim]

Hello Rela,

Thank you for reaching out for guidance on this problem. It seems like you have made a good attempt at solving it on your own, but there are a few things that need to be clarified.

Firstly, it is important to note that the force experienced by a charged object is dependent on the magnitude of its charge and the distance between it and the other charged object. In this scenario, the attractive force of 10.8 N is due to the charges on each sphere and the distance between them.

Now, let's break down the steps to finding the electric force on each sphere.

Step 1: Finding the total charge on the two spheres
From the given information, we know that the total charge on the two spheres is -24 μC. This means that the sum of the charges on both spheres is equal to -24 μC.

Step 2: Setting up the equations
We can use the equation for electric force, F = k(q1q2)/r^2, where k is the Coulomb's constant, q1 and q2 are the charges on the two spheres, and r is the distance between them.

Step 3: Solving for the charges on each sphere
Since both spheres are identical, we can assume that they have the same charge magnitude, denoted as q. Therefore, we can set up the following equations:

F = k(q)(q)/r^2 = 10.8 N
q + q = -24 μC

Solving for q, we get q = -12 μC.

Step 4: Finding the electric force on each sphere
Now that we know the magnitude of the charge on each sphere, we can plug it into the electric force equation to find the force on each sphere:

F = k(-12 μC)(-12 μC)/0.60^2 m = 10.8 N

Therefore, the electric force on each sphere is 10.8 N, as stated in the problem.

Step 5: The role of the conducting wire
You are correct in thinking that the conducting wire will conduct away all the negative charges from one sphere to the positively charged sphere. However, this process happens very quickly, and at any given moment, the force on each sphere remains the same. This is because the force is dependent on the magnitude of the charge, which remains constant even as the charges are redistributed.

I hope this explanation helps clarify your