3. An infinitely long solid cylindrical insulator of radius a has nonuniform volume charge density p(r) = Po (1-²) where r is the radial distance from the axis of the cylinder and po is a positive constant. (a) Use Gauss's law to find the electric field inside and outside the cylinder. (Hint: the charge density is nonuniform, like in Problem 2, so you have to integrate to find the charge enclosed by the Gaussian surface.)
3. An infinitely long solid cylindrical insulator of radius a has nonuniform volume charge density p(r) = Po (1-²) where r is the radial distance from the axis of the cylinder and po is a positive constant. (a) Use Gauss's law to find the electric field inside and outside the cylinder. (Hint: the charge density is nonuniform, like in Problem 2, so you have to integrate to find the charge enclosed by the Gaussian surface.)
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Transcribed Image Text:3. An infinitely long solid cylindrical insulator of radius a has nonuniform volume charge density
p(r) = Po
= Po (1-7)
where r is the radial distance from the axis of the cylinder and pois a positive constant.
(a) Use Gauss's law to find the electric field inside and outside the cylinder. (Hint: the
charge density is nonuniform, like in Problem 2, so you have to integrate to find the
charge enclosed by the Gaussian surface.)
(b) Find the value of r at which the electric field is maximum and find the value of that
maximum field.
(c) The cylindrical insulator is placed within an infinitely long hollow cylindrical conductor
with inner radius 2a and outer radius 3a. The cylinders are coaxial. The conductor is
neutral.
3a
2a
a
Find the surface charge densities on the inner and outer surfaces of the conductor
Expert Solution
Step 1
Solution:
a). The electric field can be obtained using the following gauss law.
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