Two small charged spheres, each with a charge of -10 μC, are 10 cm apart. Calculate the force between them.

Steps to Solve

1. Identify Known Values

We know the following:

• Charge of sphere 1: $q_1 = -10 , \mu C = -10 \times 10^{-6} , C$
• Charge of sphere 2: $q_2 = -10 , \mu C = -10 \times 10^{-6} , C$
• Distance between the spheres: $r = 10 , cm = 0.1 , m$

2. Use Coulomb's Law

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

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

where ( k ) is Coulomb's constant, approximately ( 8.99 \times 10^9 , N \cdot m^2/C^2 ).

3. Substitute Values into the Formula

Now substitute the known values into the formula:

$$ F = 8.99 \times 10^9 \cdot \frac{|-10 \times 10^{-6} \cdot -10 \times 10^{-6}|}{(0.1)^2} $$

4. Calculate the Force

Simplify and calculate the above expression:

$$ F = 8.99 \times 10^9 \cdot \frac{(10 \times 10^{-6})^2}{0.01} $$

$$ F = 8.99 \times 10^9 \cdot \frac{100 \times 10^{-12}}{0.01} $$

$$ F = 8.99 \times 10^9 \cdot 10^{-9} $$

5. Final Calculation

Now compute ( F ):

$$ F = 8.99 , N $$