3. A cylindrical capacitor consists of a cylinder of radius R, surrounded by a coaxial cylinder shell of inner radius R, (see Fig.3 below, R, > R,). Both cylinders have length L which we assume is much greater than the separation of the cylinders R, – R, , so that we can neglect any end effects. Now the capacitor is charged (by connecting it to a battery) so that the inner cylinder carries a charge +Q and the other one a charge -Q. Note that charges are only distributed over the outer surface of the inner cylinder and the inner surface of the outer cylinder, because of electrostatic equilibrium for these metal conductors; as a result, the electrostatic field only exists in the empty space between two cylinders. Determine: (a). The electric field E(r) as a function of the radius r measured with respect to the central axis of the cylinders. [hint: draw a proper Gaussian surface and then use Gauss's law.] (b). The potential difference (voltage) V between two cylinders. (c). The capacitance C of this cylindrical capacitor. (d). The electric energy U stored in the capacitor. 0- Rp Rp (a) (b) Fig.3 for Problem 3. (a). Cylindrical capacitor consists of two coaxial cylinder conductors. (b). The electric field lines are shown in cross-sectional view.
3. A cylindrical capacitor consists of a cylinder of radius R, surrounded by a coaxial cylinder shell of inner radius R, (see Fig.3 below, R, > R,). Both cylinders have length L which we assume is much greater than the separation of the cylinders R, – R, , so that we can neglect any end effects. Now the capacitor is charged (by connecting it to a battery) so that the inner cylinder carries a charge +Q and the other one a charge -Q. Note that charges are only distributed over the outer surface of the inner cylinder and the inner surface of the outer cylinder, because of electrostatic equilibrium for these metal conductors; as a result, the electrostatic field only exists in the empty space between two cylinders. Determine: (a). The electric field E(r) as a function of the radius r measured with respect to the central axis of the cylinders. [hint: draw a proper Gaussian surface and then use Gauss's law.] (b). The potential difference (voltage) V between two cylinders. (c). The capacitance C of this cylindrical capacitor. (d). The electric energy U stored in the capacitor. 0- Rp Rp (a) (b) Fig.3 for Problem 3. (a). Cylindrical capacitor consists of two coaxial cylinder conductors. (b). The electric field lines are shown in cross-sectional view.
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![3.
A cylindrical capacitor consists of a cylinder of radius R, surrounded by a coaxial
cylinder shell of inner radius R.(see Fig.3 below, R. > R,). Both cylinders have length L which
we assume is much greater than the separation of the cylinders R. – R,, so that we can neglect any
end effects. Now the capacitor is charged (by connecting it to a battery) so that the inner cylinder
carries a charge +Q and the other one a charge -Q. Note that charges are only distributed over the
outer surface of the inner cylinder and the inner surface of the outer cylinder, because of electrostatic
equilibrium for these metal conductors; as a result, the electrostatic field only exists in the empty
space between two cylinders. Determine:
(a). The electric field E(r) as a function of the radius r measured with respect to the central axis of the
cylinders. [hint: draw a proper Gaussian surface and then use Gauss's law.]
(b). The potential difference (voltage) V between two cylinders.
(c). The capacitance C of this cylindrical capacitor.
(d). The electric energy U stored in the capacitor.
(a)
(b)
Fig.3 for Problem 3.
(a). Cylindrical capacitor consists of two coaxial cylinder conductors.
(b). The electric field lines are shown in cross-sectional view.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44eb136a-a338-46b8-9b55-ea62f59bf314%2Ff64eed15-cc45-4423-a5cf-83da79a443d0%2Fh5k6wc_processed.png&w=3840&q=75)
Transcribed Image Text:3.
A cylindrical capacitor consists of a cylinder of radius R, surrounded by a coaxial
cylinder shell of inner radius R.(see Fig.3 below, R. > R,). Both cylinders have length L which
we assume is much greater than the separation of the cylinders R. – R,, so that we can neglect any
end effects. Now the capacitor is charged (by connecting it to a battery) so that the inner cylinder
carries a charge +Q and the other one a charge -Q. Note that charges are only distributed over the
outer surface of the inner cylinder and the inner surface of the outer cylinder, because of electrostatic
equilibrium for these metal conductors; as a result, the electrostatic field only exists in the empty
space between two cylinders. Determine:
(a). The electric field E(r) as a function of the radius r measured with respect to the central axis of the
cylinders. [hint: draw a proper Gaussian surface and then use Gauss's law.]
(b). The potential difference (voltage) V between two cylinders.
(c). The capacitance C of this cylindrical capacitor.
(d). The electric energy U stored in the capacitor.
(a)
(b)
Fig.3 for Problem 3.
(a). Cylindrical capacitor consists of two coaxial cylinder conductors.
(b). The electric field lines are shown in cross-sectional view.
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