To calculate the electric flux through a Gaussian surface, we need to find the electric field and the area of the surface. From the given figure, we can see that the Gaussian surface is a sphere centered at the charge q1.
1. Electric Field:
The electric field due to a point charge q at a distance r from it is given by the equation E = k*q/r^2, where k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2). The electric field due to q1 at the Gaussian surface is the same as the electric field at any point on the Gaussian surface. The electric field is radially outward, and its magnitude does not depend on the direction of the Gaussian surface. Thus, the electric field at the Gaussian surface is E1 = k*q1/r^2.
2. Area of the Surface:
The Gaussian surface is a sphere centered at q1, which means it encloses the charge q2. The area of a sphere is given by the equation A = 4πr^2, where r is the radius of the sphere. From the figure, we can see that the radius of the Gaussian surface is R.
3. Electric Flux:
The electric flux (Φ) through a closed surface is given by the equation Φ = E * A * cos(θ), where E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal. In this case, the electric field is radially outward, and the Gaussian surface is spherical. Therefore, the angle θ between the electric field and the surface normal is 0 degrees (cos(θ) = 1).
The electric flux through the Gaussian surface can be calculated as follows:
Φ = E * A * cos(θ) = (k*q1/R^2) * (4πR^2) * cos(0) = (k*q1) * (4πR^2) = (9 × 10^9 Nm^2/C^2) * q1 * (4πR^2).
Therefore, the electric flux through the Gaussian surface shown in the figure is (9 × 10^9 Nm^2/C^2) * q1 * (4πR^2).
Calculate the electric flux through the Gaussian surface shown in the figure below .
q12.png
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