## 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!*

**Jump to the problem**

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

**Want to get a full PDF with solutions? Read THIS.**

*The comments appending particular solutions are due to the respective users. Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 2008 by ETS.*

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 .