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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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11

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Line, surface and volume integrals

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11.1  The vector field F is defined by

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Calculate ∇ × F and deduce that F can be written F = ∇ϕ. Determine the form of ϕ.

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With F as given, we calculate the curl of F to see whether or not it is the zero vector:

The fact that it is implies that F can be written as ∇ϕ for some scalar ϕ.

The form of ϕ(x, y, z) is ...

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