a charge of 1.0x10^-6 uC is located inside a sphere. What is the flux through the sphere?
To calculate the flux through a sphere, we need to use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε₀):
Φ = Q / ε₀
In this case, we have a charge of 1.0x10^-6 uC located inside a sphere. The unit "uC" stands for microCoulombs, which is equivalent to 1.0x10^-6 C. Therefore, the charge Q is 1.0x10^-6 C.
Now, we need to determine the permittivity of free space (ε₀). The value of ε₀ is approximately 8.854x10^-12 C²/N·m².
Using Gauss's Law, we can calculate the flux (Φ):
Φ = Q / ε₀
Φ = (1.0x10^-6 C) / (8.854x10^-12 C²/N·m²)
Calculating the above expression gives:
Φ ≈ 1.13x10^5 N·m²/C
Therefore, the flux through the sphere is approximately 1.13x10^5 N·m²/C.
To find the flux through a sphere due to an electric charge, we can use Gauss's Law.
Gauss's Law states that the total electric flux through a closed surface is equal to the charge enclosed by that surface divided by the electric constant (also known as the permittivity of free space, ε₀).
The formula for the total electric flux (Φ) through a closed surface is:
Φ = (Q_enclosed) / ε₀
In this case, the charge enclosed (Q_enclosed) is 1.0x10^-6 uC (microcoulombs). However, we need to convert that charge to Coulombs before using the equation.
1 microcoulomb (uC) = 1x10^-6 Coulombs (C)
Therefore, Q_enclosed = 1.0x10^-6 C
The electric constant or the permittivity of free space (ε₀) is approximately 8.854x10^-12 C²/(N*m²).
Using the values in the formula, we have:
Φ = (1.0x10^-6 C) / (8.854x10^-12 C²/(N*m²))
Calculating this expression will give us the flux through the sphere in units of Newton-meters squared per Coulomb (N*m²/C).