To determine the force of repulsion between two charged spheres, we can use Coulomb's Law, which states that the force \( F \) between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. However, when dealing with charged spheres, we need to consider how the charge is distributed over their surfaces.
Understanding Charge Distribution
When you have point charges, the entire charge is concentrated at a single point. In contrast, when you have charged spheres, the charge is distributed uniformly over the surface of the spheres. For spheres, as long as the distance between their centers is greater than the sum of their radii, we can treat them as point charges for the purpose of calculating the force between them.
Given Information
- Initial force of repulsion \( F \) when point charges are 2m apart.
- Radius of each sphere = 50 cm = 0.5 m.
- Distance between the centers of the spheres = 2m.
Applying Coulomb's Law
The formula for Coulomb's Law is given by:
F = k * (|q1 * q2|) / r²
Where:
- F is the force between the charges.
- k is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)).
- q1 and q2 are the magnitudes of the charges.
- r is the distance between the centers of the charges.
Calculating the New Force
Since the distance between the centers of the spheres is still 2m, which is greater than the sum of their radii (0.5m + 0.5m = 1m), we can treat the spheres as point charges. Therefore, the force of repulsion between the two spheres will remain the same as that between the original point charges.
Thus, the force of repulsion between the two spheres will still be:
F = F
Conclusion
In summary, replacing point charges with uniformly charged spheres of the same charge and maintaining the same distance between their centers means that the force of repulsion remains unchanged. Therefore, the force of repulsion between the two spheres will still be \( F \).
