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Find the potential outside an infinitely long metal pipe,

Chapter 3, Problem 25P

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QUESTION:

Problem 25P

Find the potential outside an infinitely long metal pipe, of radius R, placed at right angles to an otherwise uniform electric field E0. Find the surface charge induced on the pipe. [Use your result from Prob. 3.24.]

reference prob 3.24

Solve Laplace’s equation by separation of variables in cylindrical coordinates, assuming there is no dependence on z (cylindrical symmetry). [Make sure you find all solutions to the radial equation; in particular, your result must accommodate the case of an infinite line charge, for which (of course) we already know the answer.]

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QUESTION:

Problem 25P

Find the potential outside an infinitely long metal pipe, of radius R, placed at right angles to an otherwise uniform electric field E0. Find the surface charge induced on the pipe. [Use your result from Prob. 3.24.]

reference prob 3.24

Solve Laplace’s equation by separation of variables in cylindrical coordinates, assuming there is no dependence on z (cylindrical symmetry). [Make sure you find all solutions to the radial equation; in particular, your result must accommodate the case of an infinite line charge, for which (of course) we already know the answer.]

ANSWER:

Solution 25P

Step 1 of 5

To find the potential outside for an infinitely long metal pipe of radius ‘R’ with an uniform electric field.

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