Using Gauss's Law
Gauss's law is usually written as an equation in the form
- For this equation, specify what each term in this equation means
and how it is to be calculated when doing some specific (but arbitrary
- not a special case!) calculation.
A long thin cylindrical shell of length L and radius R with L>>R
is uniformly covered with a charge Q. If we look for the field near to
the cylinder somewhere about the middle, we can treat the cylinder as if
it were an infinitely long cylinder. Using this assumption, we can calculate
the magnitude and direction of the field at a point a distance d from the
axis of the cylinder (outside the cylindrical shell, i.e., L>>d
> R but d not very close to R) using Gauss's Law. Do so by explicitly
following the steps below.
- Select an appropriate Gaussian surface. Explain why you chose it.
- Carry out the integral on the left side of the equation, expressing
it in terms of the unknown value of the magnitude of the E field.
- What is the relevant value of q for your surface?
- Use your results in (c) and (d) in the equation and solve for the magnitude
Note to the instructor: Gauss's Law can be very difficult for students in an introductory physics class. They are not comfortable with integrals. Even if they have studied integrals, calculating an integral symbolically and finding an unknown from under the integral is rarely done in a math class. This helps work through some of the barriers.
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Page last modified
October 31, 2002: E19