Two point charges of +2 μC and +6 μC repel each other with a force of 12 N. If each is given an additional charge of -4 μC, what will be the new force?

To find the new force between the two point charges after adding the additional charges, we can use Coulomb's Law, which states that the force between two charges is given by:

Formula for Coulomb's Law

The formula is:

F = k * |q1 * q2| / r²

where:

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

Initial Charges and Force

The initial charges are:

• q1 = +2 μC = +2 x 10^-6 C
• q2 = +6 μC = +6 x 10^-6 C

Given that the force between them is 12 N, we can find the distance r using the initial values:

Calculating Distance

Using the initial force:

12 N = k * |(2 x 10^-6) * (6 x 10^-6)| / r²

Rearranging gives:

r² = k * (2 x 10^-6) * (6 x 10^-6) / 12

New Charges

After adding -4 μC to each charge, the new charges become:

• New q1 = +2 μC - 4 μC = -2 μC
• New q2 = +6 μC - 4 μC = +2 μC

Calculating New Force

Now, we can calculate the new force:

F' = k * |(-2 x 10^-6) * (2 x 10^-6)| / r²

Since the charges are now one negative and one positive, they will attract each other. The absolute value of the product of the charges is:

|(-2 x 10^-6) * (2 x 10^-6)| = 4 x 10^-12 C²

Final Calculation

Substituting into the formula:

F' = k * (4 x 10^-12) / r²

Since we already calculated r² from the initial force, we can use that value here. The new force will be:

F' = 12 N * (4 x 10^-12) / (12 N)

Thus, the new force will be:

F' = 4 N

Summary

After adding -4 μC to each charge, the new force between the charges will be 4 N, and they will attract each other.