A point charge of +5 μC is located at the center of a sphere with a radius of 12 cm . What is the electric flux through the surface of this sphere ?
Phi = EA = [kq/r(sqr)] * [4(pi) r(sqr)] = 4 kq(pi)
= 4 * 9e9 * 5e-6 * 3.141 = 5.7e5
Note r cancels
To calculate the electric flux through the surface of the sphere, we can use Gauss's law.
Step 1: Gauss's law states that the electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of free space (ε0).
Step 2: Determine the total charge enclosed by the sphere. In this case, there is a point charge located at the center of the sphere with a charge of +5 μC. This charge is entirely enclosed by the sphere, so the total charge enclosed is 5 μC.
Step 3: Find the permittivity of free space (ε0). The permittivity of free space is a physical constant with a value of approximately 8.854 x 10^-12 C^2/(N·m^2).
Step 4: Calculate the electric flux through the surface of the sphere using the formula: electric flux = (total charge enclosed) / (permittivity of free space).
electric flux = (5 μC) / (8.854 x 10^-12 C^2/(N·m^2)).
Calculating this expression will give us the value of the electric flux through the surface of the sphere.
To calculate the electric flux through the surface of a sphere, we can use Gauss's Law, which states that the electric flux (Φ) through a closed surface is equal to the charge enclosed (Q) divided by the permittivity of free space (ε₀).
The formula for electric flux is given by:
Φ = Q / ε₀
In this case, we have a point charge of +5 μC located at the center of the sphere. Since the charge is at the center, it is equally spaced from all points on the surface of the sphere.
Now, to calculate the electric flux, we need to determine the charge enclosed by the sphere. Since the point charge is at the center and the sphere is completely enclosing it, the entire charge is enclosed by the sphere. Therefore, the charge enclosed (Q) is equal to +5 μC.
The permittivity of free space (ε₀) is a constant with a value of approximately 8.85 x 10⁻¹² C²/(N·m²).
Now we can plug in the values into the formula:
Φ = Q / ε₀
= (+5 μC) / (8.85 x 10⁻¹² C²/(N·m²))
To simplify the units, we can convert 5 μC to Coulombs (C):
5 μC = 5 x 10⁻⁶ C
Substituting the values into the formula:
Φ = (5 x 10⁻⁶ C) / (8.85 x 10⁻¹² C²/(N·m²))
Now, we can divide the numerator by the denominator:
Φ ≈ 5.65 x 10⁶ N·m²/C²
Therefore, the electric flux through the surface of the sphere is approximately 5.65 x 10⁶ N·m²/C².