A cubical Gaussian surface surrounds three positive charges, each has a charge q1 = +4.00 × 10-12 C, and two negative charges, each has a charge q2 = −2.30 × 10-12 C as the drawing shows. What is the electric flux passing through the surface?(The permittivity of free space ε0 = 8.85×10-12C²/(N.m²))
add the charges.
flux= net charge/permitivity
To find the electric flux passing through the surface, we can use Gauss's Law, which states that the total electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space.
1. Calculate the total charge enclosed by the surface:
- There are three positive charges, each with a charge of q1 = +4.00 × 10^-12 C. So the total positive charge is Q1 = 3 * q1 = 12.00 × 10^-12 C.
- There are two negative charges, each with a charge of q2 = -2.30 × 10^-12 C. So the total negative charge is Q2 = 2 * q2 = -4.60 × 10^-12 C.
- The net charge enclosed by the surface is Q = Q1 + Q2 = 12.00 × 10^-12 C + (-4.60 × 10^-12 C) = 7.40 × 10^-12 C.
2. Calculate the electric flux passing through the surface:
- Using Gauss's Law, electric flux (Φ) = Q/ε0, where ε0 is the permittivity of free space and is equal to 8.85 × 10^-12 C²/(N.m²).
- Plug in the values: Φ = (7.40 × 10^-12 C) / (8.85 × 10^-12 C²/(N.m²)).
- Simplify the expression: Φ = 7.40 / 8.85 N*m².
- Calculate the value: Φ = 0.836 N*m².
Therefore, the electric flux passing through the surface is 0.836 N*m².
To find the electric flux passing through the surface, we can use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space.
To find the electric flux passing through the surface, we can follow these steps:
1. Calculate the net charge enclosed by the Gaussian surface. In this case, we have three positive charges of q1 = +4.00 × 10^(-12) C each, and two negative charges of q2 = -2.30 × 10^(-12) C each. Therefore, the net charge enclosed is:
q_enclosed = (3 * q1) + (2 * q2)
2. Substitute the value of the net charge enclosed into Gauss's Law equation:
Electric Flux = (q_enclosed) / ε0
3. Substitute the value of the permittivity of free space ε0 = 8.85 × 10^(-12) C²/(N.m²).
4. Calculate the electric flux using the formula:
Electric Flux = (q_enclosed) / ε0
5. Calculate the electric flux passing through the surface.
Now let's substitute the values and calculate the electric flux:
q1 = +4.00 × 10^(-12) C
q2 = -2.30 × 10^(-12) C
ε0 = 8.85 × 10^(-12) C²/(N.m²)
q_enclosed = (3 * q1) + (2 * q2) = (3 * (4.00 × 10^(-12) C)) + (2 * (-2.30 × 10^(-12) C))
Electric Flux = (q_enclosed) / ε0 = [(3 * (4.00 × 10^(-12) C)) + (2 * (-2.30 × 10^(-12) C))] / (8.85 × 10^(-12) C²/(N.m²))
Now, calculate the final value to find the electric flux passing through the surface.