In: Physics
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length ?? where ? is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?.
Part B
Find the direction of the electric field in terms of ?and the distance r from the axis of the tube forr<a.
Find the direction of the electric field in terms of and the distance from the axis of the tube for .
parallel to tube's axis | |
radially outward | |
radially inward | |
the field is zero |
Part D
Find the direction of the electric field in terms of ?and the distance r from the axis of the tube for a<r<b.
Find the direction of the electric field in terms of and the distance from the axis of the tube for .
parallel to tube's axis | |
radially outward | |
radially inward | |
the field is zero |
Part G
What is the charge per unit length on the inner surface of the tube?
Express your answer in terms of the given quantities and appropriate constants.
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?inner= |
Part H
What is the charge per unit length on the outer surface of the tube?
Express your answer in terms of the given quantities and appropriate constants.
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|||
?outer= |
PLEASE SHOW ALL WORK! Thanks!
let's choose a cylinder as the Gaussian surface that we will use
to find out the electric field in each area.
Imagine a cylinder concentric with the line of charge of radius
r< a. The charge enclosed by the cylinder is going to be aL
(where L is the length of the imaginary cylinder, much shorter than
l). The electric flux on the ends of the cylinder will be zero (the
electric field from the left and right sides will essential cancel
out because the length l is much greater than the radius). The
electric flux will be only through the curved surface of the
cylinder which has an area of 2*pi*r*L.
Plug these values into the formula: E*2*pi*r*L = a*L/e
E=2ka/r (where k = 1/(4*pi*e))
Use this same method by choosing a Gaussian surface (cylinder) with
radii of a<r<b, and r>b.
For a<r<b, the electric field will be zero (the net charge
enclosed by the Gaussian surface will be zero, electric filed
within any conductor is zero).
For r>b, E=4ka/r
B
the direction of the electric field radially outward
D
the direction of the electric field radially inward