Final answer:
The net flux through a spherical surface can be determined by calculating the flux due to each individual charge and summing them up. In this case, we have charges q = -40 pC at x = 0 and Q = +30 pC at x = 2.0 m. Using the formulas Φ = E * A and E = k * q / r^2, where k is the electrostatic constant, we can calculate the flux due to each charge and then find the net flux.
Step-by-step explanation:
To determine the net flux through a spherical surface, we need to calculate the flux due to each individual charge and then sum them up. The flux through a closed surface is given by the formula Φ = E * A, where E is the electric field and A is the area of the surface. The electric field due to a point charge q at a distance r from the charge is given by the formula E = k * q / r^2, where k is the electrostatic constant. Using this formula, we can calculate the electric field due to each charge at the surface and then sum them up to find the net flux. In this case, we have two charges, q = -40 pC and Q = +30 pC, located at x = 0 and x = 2.0 m, respectively. The radius of the spherical surface is 1.0 m.
Let's calculate the flux for each charge.
The flux due to charge q at x = 0:
E = k * q / r^2
= (9 * 10^9 N*m^2/C^2) * (-40 * 10^-12 C) / (1.0 m)^2
= -3.6 N * m^2/C
To find the area A of the surface, we use the formula A = 4 * π * r^2:
A = 4 * π * (1.0 m)^2
= 4 * 3.14 * 1.0 m^2
= 12.56 m^2
Now we can calculate the flux Φ = E * A:
Φ = (-3.6 N * m^2/C) * (12.56 m^2)
= -45.216 N * m^2/C
The flux due to charge Q at x = 2.0 m:
E = k * Q / r^2
= (9 * 10^9 N*m^2/C^2) * (30 * 10^-12 C) / (2.0 m)^2
= 3.375 N * m^2/C
A = 4 * π * (1.0 m)^2
= 4 * 3.14 * 1.0 m^2
= 12.56 m^2
Φ = (3.375 N * m^2/C) * (12.56 m^2)
= 42.3 N * m^2/C
Finally, the net flux is the sum of the fluxes due to each charge:
Net flux = Φ_q + Φ_Q
= -45.216 N * m^2/C + 42.3 N * m^2/C
= -2.916 N * m^2/C