Find the electric potential energy between two charges separated by 10 cm if charge on point A = 9 μC and charge on point B = 4 μC.

Steps to Solve

1. Identify Known Values The charges and distance are given:

   • Charge on point A, ( Q_1 = 9 , \mu C = 9 \times 10^{-6} , C )
   • Charge on point B, ( Q_2 = 4 , \mu C = 4 \times 10^{-6} , C )
   • Distance ( r = 10 , cm = 0.1 , m )

2. Use the Formula for Electric Potential Energy The formula for electric potential energy ( U ) between two point charges is: $$ U = k \frac{Q_1 Q_2}{r} $$ where ( k ) is Coulomb's constant, approximately ( 8.99 \times 10^9 , \text{N} \cdot \text{m}^2/\text{C}^2 ).

3. Substitute the Known Values into the Formula Plugging in the values: $$ U = 8.99 \times 10^9 \cdot \frac{(9 \times 10^{-6})(4 \times 10^{-6})}{0.1} $$

4. Calculate the Electric Potential Energy First, calculate the product of the charges: $$ (9 \times 10^{-6})(4 \times 10^{-6}) = 36 \times 10^{-12} , C^2 $$ Now substitute this value back into the equation: $$ U = 8.99 \times 10^9 \cdot \frac{36 \times 10^{-12}}{0.1} $$

5. Simplify and Calculate $$ U = 8.99 \times 10^9 \cdot 360 \times 10^{-12} $$ $$ U = 8.99 \times 360 \times 10^{-3} $$ $$ U \approx 3236.4 , J $$