Question

A point charge q1=5nC is located at the origin and a second point charge q2=-3nC in on the x axis at x=1.0m. what is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius a)0.5m, b)1.5 c)2.5m?

Answer 1

The total electric flux due to two point charges can be calculated using Gauss's Law. The electric flux is given by the formula Φ=E•A, where E is the electric field and A is the area of the surface. To find the electric field at any point due to a point charge, we can use the equation E=kq/r^2.

Step-by-step explanation:

The total electric flux due to two point charges can be calculated using Gauss's Law. The formula for electric flux is Φ=E•A, where E is the electric field and A is the area of the surface. To find the electric field at any point due to a point charge, we can use the equation E=kq/r^2, where k is Coulomb's constant, q is the charge, and r is the distance from the charge.

For the first case, when the radius of the spherical surface is 0.5m, the electric field at that point due to q1 is E1=kq1/r^2 and the electric field at that point due to q2 is E2=kq2/(r-1)^2. The total electric field at that point is E_total=E1+E2.

Using the electric field, we can calculate the electric flux Φ by multiplying the electric field by the surface area of the spherical surface. The formula for the surface area of a sphere is 4πr^2. Therefore, the total electric flux through the spherical surface is Φ_total=E_total*(4πr^2). You can now calculate the electric flux for each case by substituting the values of q1, q2, and r into the equations.

Answer 2

To calculate the total electric flux due to the two point charges, we can use Gauss's Law. The electric flux through a closed surface is given by the equation:

Φ = q_enclosed / ε₀

Where Φ is the electric flux, q_enclosed is the charge enclosed by the surface, and ε₀ is the permittivity of free space.

In this case, since we have two point charges, we need to consider the flux due to each charge separately and then add them together.

For a spherical surface centered at the origin, the electric flux due to a point charge q is given by:

Φ = q / (4πε₀r²)

where r is the radius of the spherical surface.

Let's calculate the total electric flux for each radius:

a) For r = 0.5m:

The electric flux due to q1 is:

Φ₁ = q₁ / (4πε₀r²) = (5nC) / (4πε₀(0.5m)²)

The electric flux due to q2 is:

Φ₂ = q₂ / (4πε₀r²) = (-3nC) / (4πε₀(0.5m)²)

The total electric flux Φ = Φ₁ + Φ₂

b) For r = 1.5m:

The electric flux due to q1 is:

Φ₁ = q₁ / (4πε₀r²) = (5nC) / (4πε₀(1.5m)²)

The electric flux due to q2 is:

Φ₂ = q₂ / (4πε₀r²) = (-3nC) / (4πε₀(1.5m)²)

The total electric flux Φ = Φ₁ + Φ₂

c) For r = 2.5m:

The electric flux due to q1 is:

Φ₁ = q₁ / (4πε₀r²) = (5nC) / (4πε₀(2.5m)²)

The electric flux due to q2 is:

Φ₂ = q₂ / (4πε₀r²) = (-3nC) / (4πε₀(2.5m)²)

The total electric flux Φ = Φ₁ + Φ₂