Module 1 : A Crash Course in Vectors
Lecture 4 : Gradient of a Scalar Function

Example 18 :
In Example 13 we found that the surface integral of a vector field $x\hat\imath + y\hat\jmath + z\hat k$over a cylinder of radius $R$and height $h$is $3\pi R^2h$. Verify this result using the divergence theorem.


Solution :

In Example 16 we have seen that the divergence of the field vector is 3. Since the integrand is constant, the volume integral is $3V = 3\pi R^2h$.

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