Two identical metallic spheres, labeled A and B, carry excess charges of +1µC (sphere A) and +3µC (sphere b). What feels a stronger repuslive force ... two pith balls each with +3nC of excess charge that are 10 cm apart, or two pith balls each with +2nC of charge that are 6 cm apart? For the pith balls, what is the magnitude of the repulsive force on each of the +3nC pith balls in ?
The magnitude of the repulsive force between two charged objects is given by Coulomb's Law:
\[F = k \cdot \frac{q_1 \cdot q_2}{r^2}\]
Where:
- \(F\) is the magnitude of the repulsive force
- \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, N \cdot m^2/C^2\))
- \(q_1\) and \(q_2\) are the charges on the two objects
- \(r\) is the distance between the two objects
For the two +3nC pith balls that are 10 cm apart:
- \(q_1 = q_2 = +3nC = 3 \times 10^{-9} C\)
- \(r = 0.1 m\)
\[F_1 = (8.99 \times 10^9) \cdot \frac{(3 \times 10^{-9}) \cdot (3 \times 10^{-9})}{(0.1)^2} = 810 N\]
For the two +2nC pith balls that are 6 cm apart:
- \(q_1 = q_2 = +2nC = 2 \times 10^{-9} C\)
- \(r = 0.06 m\)
\[F_2 = (8.99 \times 10^9) \cdot \frac{(2 \times 10^{-9}) \cdot (2 \times 10^{-9})}{(0.06)^2} = 888.89 N\]
Therefore, the pith balls with +2nC of charge that are 6 cm apart feel a stronger repulsive force (888.89 N) compared to the pith balls with +3nC of charge that are 10 cm apart (810 N).