A sphere has a radius of 0.20 meters and has a uniform surface charge density equal to 6.3 micro coulombs per meter squared. A second point charge has a magnitude of 0.58 micro coulombs and is 0.61 meters away from the center of the sphere. Find the magnitude of the force exerted by the sphere on the second point charge.
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.
To find the magnitude of the force exerted by the sphere on the second point charge, you can make use of Coulomb's Law. Coulomb's law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
F is the magnitude of the force
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
First, let's calculate the charge of the sphere. The surface charge density is given as 6.3 micro coulombs per square meter. To find the total charge of the sphere, we need to multiply this surface charge density by the surface area of the sphere.
The surface area of a sphere is given by:
A = 4πr^2
Where:
A is the surface area
r is the radius
Substituting the known values:
A = 4π(0.20^2) = 4π(0.04) = 0.5026 m^2
Now we can find the charge of the sphere:
Charge = Surface Charge Density * Surface Area
Charge = (6.3 x 10^-6 C/m^2) * (0.5026 m^2)
Charge = 3.16038 x 10^-6 C
Now we have the magnitudes of the two charges:
q1 (sphere) = 3.16038 x 10^-6 C
q2 (second point charge) = 0.58 x 10^-6 C
Next, we need to calculate the distance between the charges:
r = 0.61 m
Finally, we can substitute these values into Coulomb's Law to find the magnitude of the force:
F = (8.99 x 10^9 N m^2/C^2) * ((3.16038 x 10^-6 C) * (0.58 x 10^-6 C)) / (0.61 m)^2
Simplifying the calculation will give you the magnitude of the force exerted by the sphere on the second point charge.