Finding the electric force on each sphere

The force will act on each sphere equally with -12 uC and will make the spheres get closer to each other, until they reach equilibrium at a distance of 0.60 m.In summary, two identical small conducting spheres with a total charge of -24 μC are separated by 0.60 m and connected by a slender conducting wire. After the wire is removed, the spheres each have a charge of -12 μC and experience an attractive electric force of 10.8 N, causing them to move closer to each other until reaching equilibrium.
  • #1
17
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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
 
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  • #2
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.
 
  • #3


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
 

1. What is the electric force and how is it calculated?

The electric force is a fundamental force that exists between charged particles. It is calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges.

2. What are the factors that affect the electric force between two spheres?

The electric force between two spheres is affected by the magnitude of the charges on the spheres, the distance between the spheres, and the medium between the spheres.

3. How do you find the electric force on each sphere if they have different charges?

To find the electric force on each sphere, you need to use Coulomb's Law and plug in the charges of each sphere, as well as the distance between them. The force will be in the direction of the electric field lines, from the positively charged sphere to the negatively charged one.

4. Can the electric force between two spheres be repulsive?

Yes, the electric force between two spheres can be repulsive if the charges on the spheres are of the same sign. This is because like charges repel each other according to Coulomb's Law.

5. How does the electric force between two spheres change if the distance between them is halved?

If the distance between two spheres is halved, the electric force between them will quadruple. This is because the force is inversely proportional to the square of the distance, so decreasing the distance by half will result in a four-fold increase in force.

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