## GR0877 Problem 91

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**C**) When , the line integral of around any closed loop, according to Stokes’ theorem, is zero. Because of this, we can unambiguously talk about a scalar function such that .

*Found a typo? Comment!*

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We know that the curl of a gradient is always 0. Given E is the gradient of a scalar, the curl of E must be 0!

Be careful. The curl of E isn’t always zero. Recall your Maxwell Equations where

$ latex \nabla \times E=-\frac { \partial B }{ \partial t } $

which of course can be non-zero if there’s a time-varying magnetic field. But I guess it must be to have a unique solution to $ latex E=- \nabla \phi $ .

damn! my latex didn’t work! admin, can you please fix it? and thank you, generally, for the wonderful site!

Hm… Trying again:

Be careful. The curl of E isn’t always zero. Recall your Maxwell Equations where

which of course can be non-zero if there’s a time-varying magnetic field. But I guess it must be to have a unique solution to .