Can you explain the answer of this question below:Two charges of equal magnitudes and at a distance r exert a force F on each other. If the cahrges are halved and distance between them is doubled, then the new force acting on each charge isA:F/8B:F/4C:4FD:F/16The answer is d.

Question

Answer

Yes it's absolutely rt coz F is directly proportional to charges and invesersly for distance When we consider as two cases and solve it by taking the ratio of them the final answer comes

Answer

The given problem involves two charges of equal magnitudes, denoted as q, and a distance between them, denoted as r. These charges exert a force, denoted as F, on each other.

The problem states that if the charges are halved and the distance between them is doubled, we need to determine the new force acting on each charge.

To solve this problem, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:

F = k * (q1 * q2) / r^2

Where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.

Let's analyze the given changes and find the new force.

1. Halving the charges:
If the charges are halved, the new charges can be represented as q' = q/2.

2. Doubling the distance:
If the distance between the charges is doubled, the new distance can be represented as r' = 2r.

Substituting these values into Coulomb's Law, we get:

F' = k * ((q/2) * (q/2)) / (2r)^2

Simplifying the equation, we have:

F' = k * (q^2 / 4) / (4r^2)

F' = k * q^2 / (16r^2)

Comparing this equation with Coulomb's Law, we can see that the new force F' is equal to the original force F divided by 16. Mathematically, it can be represented as:

F' = F / 16

Therefore, the new force acting on each charge is F/16.

In conclusion, when the charges are halved and the distance between them is doubled, the new force acting on each charge is F/16.

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