Learning Goal: To understand the definition of electric flux, and how to calculate it.

Flux is the amount of a vector field that "flows" through a surface. We now discuss the electric flux through a surface (a quantity needed in Gauss's law): , where is the flux through a surface with differential area element , and is the electric field in which the surface lies. There are several important points to consider in this expression:

It is an integral over a surface, involving the electric field at the surface.

is a vector with magnitude equal to the area of an infinitesmal surface element and pointing in a direction normal (and usually outward) to the infinitesmal surface element.

The scalar (dot) product implies that only the component of normal to the surface contributes to the integral. That is, , where is the angle between and .

When you compute flux, try to pick a surface that is either parallel or perpendicular to , so that the dot product is easy to compute.

Two hemispherical surfaces, 1 and 2, of respective radii and , are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position due to the point charge is:

where is a constant proportional to the charge, , and is the unit vector in the radial direction

### Recently Asked Questions

- Martell Corporation's stock had a required return of 12.00% last year, when the risk-free rate was 3.00% and the market risk premium was 6.00%.Then an increase

- Stock X has a beta of 0.6 and Stock Y has a beta of 1.10.Which of the following statements must be true about these securities?(Assume the market is in

- You have recently been hired as a consultant for a personal financial planning firm.One of your first projects is creating a retirement plan for a young