The sum of two-point charges is 6 μC. They each exert a force of 0.9 N when kept apart.

Steps to Solve

1. Understanding the Forces and Charges

There are two point charges, ( q_1 ) and ( q_2 ), with a total charge of ( 6 , \mu C ). This means:

$$ q_1 + q_2 = 6 , \mu C $$

Each charge exerts a force of ( 0.9 , N ) when kept apart.

2. Applying Coulomb's Law

Coulomb's law states that the electrostatic force ( F ) between two charges is given by:

$$ F = k \frac{|q_1 q_2|}{r^2} $$

where:

• ( k ) is Coulomb's constant, approximately ( 8.99 \times 10^9 , N m^2/C^2 )
• ( r ) is the distance between the charges.

Since ( F = 0.9 , N ), we will express ( q_1 ) and ( q_2 ) in terms of one variable.

3. Substituting Variables

Let ( q_2 = 6 , \mu C - q_1 ).

Substituting ( q_2 ) into Coulomb's law gives:

$$ 0.9 = k \frac{|q_1 (6 \times 10^{-6} - q_1)|}{r^2} $$

This equation expresses the force in terms of ( q_1 ) and other known values.

4. Rearranging the Equation

Rearranging gives:

$$ |q_1 (6 \times 10^{-6} - q_1)| = \frac{0.9 r^2}{k} $$

To find specific values for ( q_1 ) and ( q_2 ), we'd typically need more information, like the distance ( r ).

5. Conclusion

Without additional information such as the distance ( r ), we cannot solve directly for ( q_1 ) and ( q_2 ). However, you can establish relationships between the values if ( r ) is given.