Surface Integral/Examples/Magnetic Flux
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Example of Surface Integral
Let $\mathbf M$ be an magnetic field acting over a region of space $R$.
Let $S$ be a surface through which $\mathbf M$ acts.
Let $\d S$ be a small element of $S$ whose center is at a point $P$.
Then the magnetic flux through $S$ to which $\mathbf M$ gives rise is given by the surface integral:
- $\ds \iint_S \mathbf M \cdot \mathbf {\hat n} \rd S$
where $\mathbf {\hat n}$ denotes the unit normal to $S$ at $\d S$ in the direction of flow of $\mathbf M$.
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals