Question

Two-point charges of 6uC and 9uC
separated by 10 cm repel each other with
some force F. If a charge of - 4uC is
added with each of them, then the force
between them is 20 N. Calculate the
initial force exists between them before
adding the charge.​

Answer 1

Given:

Two-point charges of 6uC and 9uC separated by 10 cm repel each other with some force F. If a charge of - 4uC is added with each of them, then the force between them is 20 N.

To find:

Calculate the initial force exists between them before adding the charge.​

Solution:

From given, we have,

q1 = 6μC

q2 = 9μC

d = 10 cm (distance between the charges)

Initial force = F

-4μC is added

Then, the new force = Fnew = 20 N

Using Coulomb's law, we have,

F = k q1×q2 / d²

F = k × 6μ × 9μ / 10²

Fnew = 20 = k × (6μ - 4μ) × (9μ - 4μ) / 10²

Fnew = k × 2μ × 5μ / 10²

Fnew / F = [ k × 2μ × 5μ / 10² ] / [  k × 6μ × 9μ / 10² ]

Fnew / F = (2 × 5) / (6 × 9)

F = 54/10 × Fnew = 54/10 × 20

∴ F = 108 N.

∴ The initial force is 108 N.