force between two identical spheres charged with same charge is F. If 50% charge of one sphere is transferred to the other sphere then the new force will be:
Question
force between two identical spheres charged with same charge is F. If 50% charge of one sphere is transferred to the other sphere then the new force will be:
Solution
To find the new force between the two spheres, we can use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's assume that the original charge on each sphere is Q. Since both spheres have the same charge, the total charge before any transfer is 2Q.
According to the problem, 50% of the charge from one sphere is transferred to the other sphere. This means that one sphere now has a charge of Q + 0.5Q = 1.5Q, and the other sphere has a charge of Q - 0.5Q = 0.5Q.
Now, let's calculate the new force between the spheres using Coulomb's law. The formula for the force between two charged spheres is:
F = (k * (q1 * q2)) / r^2
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the distance between the spheres.
Since the spheres are identical, the distance between them remains the same. Therefore, the only change is in the charges.
Substituting the new charges into the formula, we get:
New force = (k * (1.5Q * 0.5Q)) / r^2
Simplifying this expression, we have:
New force = (k * 0.75Q^2) / r^2
So, the new force between the spheres is 0.75 times the original force (F).
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