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Vector Area

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One of the results of this problem is required for a later one on magnetic moments that I’d like to do.

Question: Vector Area. ([1] pr. 1.61)

The integral

\begin{equation}\label{eqn:vectorAreaGriffiths:20} \Ba = \int_S d\Ba, \end{equation}

is sometimes called the vector area of the surface \( S \).

(a)

Find the vector area of a…

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Electric field due to spherical shell

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Here’s a problem (2.7) from [1], to calculate the field due to a spherical shell. The field is

\begin{equation}\label{eqn:griffithsEM2_7:20} \BE = \frac{\sigma}{4 \pi \epsilon_0} \int \frac{(\Br – \Br’)}{\Abs{\Br – \Br’}^3} da’, \end{equation}

where \( \Br’ \) is the position to the area element on the shell. For the test position, let \(…

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