To find the magnitude of the force exerted by the sphere on the second point charge, we can use Coulomb's law.
Coulomb's law states that the magnitude of the force between two point charges is given by:
F = k * q1 * q2 / r^2
where:
- F is the magnitude of the force,
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
In this case, the sphere has a uniform surface charge density. The charge on the sphere can be found by multiplying the surface charge density by the surface area of the sphere:
q1 = charge density * surface area
The surface area of a sphere is given by:
surface area = 4 * π * r^2
In this case, the radius of the sphere is 0.20 meters, and the surface charge density is 6.3 micro coulombs per meter squared.
Let's calculate the charge on the sphere:
surface area = 4 * π * (0.20)^2 = 0.50265 m^2
q1 = 6.3 * 10^-6 C/m^2 * 0.50265 m^2 = 3.167745 * 10^-6 C
Now, we can calculate the magnitude of the force exerted by the sphere on the second point charge:
F = (9 x 10^9 Nm^2/C^2) * (3.167745 * 10^-6 C) * (0.58 * 10^-6 C) / (0.61 m)^2
F = 6.717036 * 10^-4 N
Therefore, the magnitude of the force exerted by the sphere on the second point charge is approximately 0.0006717 N.