To find the distance between the two charged spheres and the force on the second sphere due to the first, we can use Coulomb's Law. This law describes the electrostatic force between two point charges and is given by the formula:
Coulomb's Law
The formula is expressed as:
F = k * |q1 * q2| / r²
Where:
- F is the magnitude of the electrostatic force between the charges.
- k is Coulomb's constant, approximately 8.99 x 10^9 N m²/C².
- q1 and q2 are the amounts of charge on the two spheres.
- r is the distance between the centers of the two charges.
Part a: Finding the Distance Between the Spheres
Given:
- q1 = 0.4 micro coulomb = 0.4 x 10^-6 C
- q2 = -0.8 micro coulomb = -0.8 x 10^-6 C
- F = 0.2 N
We can rearrange Coulomb's Law to solve for r:
r = sqrt(k * |q1 * q2| / F)
Now, substituting the values:
r = sqrt((8.99 x 10^9 N m²/C²) * |(0.4 x 10^-6 C) * (-0.8 x 10^-6 C)| / 0.2 N)
Calculating the product of the charges:
|q1 * q2| = |(0.4 x 10^-6) * (-0.8 x 10^-6)| = 0.32 x 10^-12 C²
Now substituting this back into the equation for r:
r = sqrt((8.99 x 10^9) * (0.32 x 10^-12) / 0.2)
Calculating this gives:
r = sqrt((8.99 x 10^9) * (0.32 x 10^-12) / 0.2) = sqrt(1.4384 x 10^-2) ≈ 0.1198 m
Thus, the distance between the two spheres is approximately 0.12 m or 12 cm.
Part b: Force on the Second Sphere Due to the First
According to Newton's Third Law, the force exerted by the first sphere on the second is equal in magnitude and opposite in direction to the force exerted by the second sphere on the first. Therefore, the force on the second sphere due to the first is also 0.2 N, but in the opposite direction.
In summary, the distance between the two spheres is approximately 0.12 m, and the force on the second sphere due to the first is 0.2 N, directed towards the first sphere. This illustrates the fundamental principles of electrostatics and the interactions between charged objects.
