The divergence theorem often comes in handy when evaluating surface integrals. For example, suppose an electric field is given by (omitting any units in the following) E 3ri + 2yj + Oz, %3! and supposé you are asked to find the total electric flux g through the surface S of a sphere of radius 3 centered at the origin. This means that you would need to evaluate the surface integral DE = /| (3ri + 2yj) - nds, where the unit vector n points outward from the sphere. Direct evaluation of this integral would obviously be rather tedious: we would need to parametrize the surface and then calculate all the dot products. Here, the divergence theorem comes to our rescue. Use it to show that e = 180m.

The divergence theorem often comes in handy when evaluating surface integrals. For example, suppose an electric field is given by (omitting any units in the following) E 3ri + 2yj + Oz, %3! and supposé you are asked to find the total electric flux g through the surface S of a sphere of radius 3 centered at the origin. This means that you would need to evaluate the surface integral DE = /| (3ri + 2yj) - nds, where the unit vector n points outward from the sphere. Direct evaluation of this integral would obviously be rather tedious: we would need to parametrize the surface and then calculate all the dot products. Here, the divergence theorem comes to our rescue. Use it to show that e = 180m.