# Clarification on Electric Flux

• gambit1414
In summary, the conversation discusses the flux of two spheres with different diameters and equal charges. One person suggests that the fluxes are equal due to the equation for total flux, but the other person raises the point that the electric field on the larger sphere may be weaker. The use of equations clarifies that the flux is equal to the charge contained within the surface and that the magnitude of the flux is affected by the radius of the sphere.

#### gambit1414

A question has 2 spheres of different diameters surrounding equal charges 'q'. Diameter of sphere A is smaller than diameter of sphere B. Now are the flux for both equal or not? I think they are equal because total flux = Qenclose/ epsilon-knot, so flux only depends on the charges. But then again the electric field on the bigger sphere (B) would be weaker than the E-field on sphere A examining the equation for E-field and flux is equal to the surface integral of E dot ds. So I'm questioning which is the correct answer. Thank You.

Let us take a look at some equations. That should clear up your question:

The surface integral of the flux (D) out of a closed surface (S) is equal to the charge (Q) contained within the surface (Gauss' Law):
$$\int \int_s \vec{D} d \vec{S} = Q$$

This can be solved for D as follows if the surface is a sphere where r is the radius of the sphere:

$$\vec{D} = \frac{Q}{4\pi r^2} \vec{a}$$

Now look at equation 2. What affect does r have on the magnitude of the flux?

Your understanding of electric flux is correct - it is a measure of the total electric field passing through a given surface. In this scenario, the charges on both spheres are the same, so the total flux should be equal for both spheres. However, the electric field on the surface of sphere B would be weaker than on the surface of sphere A due to the larger surface area of sphere B. This means that the electric flux per unit area would be lower for sphere B compared to sphere A. So while the total flux is equal, the flux per unit area is not. Both answers are technically correct, but it is important to specify which measure of flux you are referring to.

## 1. What is electric flux?

Electric flux is a measure of the amount of electric field passing through a given surface. It is defined as the product of the electric field and the perpendicular area of the surface it passes through.

## 2. How is electric flux calculated?

The electric flux passing through a surface can be calculated by taking the dot product of the electric field and the surface area vector, and then integrating over the entire surface.

## 3. What is the unit of electric flux?

The unit of electric flux is volts x meters (V x m) or newton x meters squared per coulomb (N x m2/C).

## 4. What is the significance of electric flux?

Electric flux helps in understanding the strength and direction of the electric field passing through a surface. It is also used in Gauss's law to calculate the total electric charge enclosed by a closed surface.

## 5. How does the presence of a charged object affect electric flux?

The presence of a charged object can alter the direction and magnitude of the electric flux passing through a surface. The direction of the electric flux is always from higher to lower potential, so a positive charge will have electric flux directed outward and a negative charge will have electric flux directed inward.