two charges 10 micro columb and 18 micro columb are 3m part in air . find force of replulsion between them ?

To find the force of repulsion between two charges, we can use Coulomb's Law, which describes the electrostatic force between two point charges. The formula is given by:

Coulomb's Law Formula

The formula is expressed as:

F = k * |q1 * q2| / r²

Where:

• F is the force between the charges (in Newtons).
• k is Coulomb's constant, approximately 8.99 x 10^9 N m²/C².
• q1 and q2 are the magnitudes of the charges (in Coulombs).
• r is the distance between the charges (in meters).

Given Values

In your case, we have:

• q1 = 10 microcoulombs = 10 x 10^-6 C
• q2 = 18 microcoulombs = 18 x 10^-6 C
• r = 3 m

Calculating the Force

Now, let's plug these values into the formula:

F = (8.99 x 10^9 N m²/C²) * |(10 x 10^-6 C) * (18 x 10^-6 C)| / (3 m)²

First, calculate the product of the charges:

|q1 * q2| = |(10 x 10^-6) * (18 x 10^-6)| = 180 x 10^-12 C²

Next, calculate the square of the distance:

(3 m)² = 9 m²

Now, substitute these values back into the formula:

F = (8.99 x 10^9) * (180 x 10^-12) / 9

Calculating this step-by-step:

• First, calculate the numerator: 8.99 x 10^9 * 180 x 10^-12 = 1618.2 x 10^-3
• Now, divide by 9: F = 1618.2 x 10^-3 / 9 = 179.8 x 10^-3 N

Final Result

Thus, the force of repulsion between the two charges is approximately 0.1798 N. This means that the two charges will push away from each other with a force of about 0.18 Newtons.

This calculation illustrates how electric forces can be significant even at relatively small distances, highlighting the power of electrostatic interactions. If you have any further questions or need clarification on any step, feel free to ask!