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A student applies Gauss's law to a finite line charge with a coaxial cylinder and obtains the infinite-line result. The error is that

  • A.the ends of the cylinder carry flux that has been ignored
  • B.the enclosed charge has been computed for the wrong length
  • C.the field is not constant along the length of the finite line
  • D.Gauss's law does not apply to a line charge at all

Answer: C

Near the ends of a finite line the field has an axial component and its magnitude varies along the cylinder, so it cannot be taken outside the integral. The infinite-line formula is a good approximation only near the middle of a long line.

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