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10 Nov 2019
A coaxial cubic consists of two conductors separated by an insulating material or dielectric. When the inner and outer conductors earn equal and opposite charges per unit length, the cable acts as a capacitor. In this problem you derive expressions first for the electric field between the conductors and then for the capacitance per unit length. Suppose the charge per unit length is + lambda C/m on the inner conductor, which has a radius a m, and - lambda on the outer conductor, of radius b m. Choose a suitable Gaussian surface and apply Gauss's law to show that the electric field between the conductors is given by (where r is radius, and is between a and b) Since C=Q/V, then to find the capacitance per unit length, you need lambda/V, and so you need to find V, the potential difference between the two conductors. Recall that Integration is necessary because the electric field between the conductors is not uniform. Substitute your expression for E and integrate to get Delta V. Which conductor is at the higher potential? Finally obtain your expression for capacitance per unit length. Check that it depends only on the dimensions of the cable and epsilon 0 (multiplied by a dielectric constant if there is an insulating material between the conductors) What is the capacitance of a 50 m long cable with a = 1mm and b = 3mm, filled with a nylon dielectric of dielectric constant 3.5?
A coaxial cubic consists of two conductors separated by an insulating material or dielectric. When the inner and outer conductors earn equal and opposite charges per unit length, the cable acts as a capacitor. In this problem you derive expressions first for the electric field between the conductors and then for the capacitance per unit length. Suppose the charge per unit length is + lambda C/m on the inner conductor, which has a radius a m, and - lambda on the outer conductor, of radius b m. Choose a suitable Gaussian surface and apply Gauss's law to show that the electric field between the conductors is given by (where r is radius, and is between a and b) Since C=Q/V, then to find the capacitance per unit length, you need lambda/V, and so you need to find V, the potential difference between the two conductors. Recall that Integration is necessary because the electric field between the conductors is not uniform. Substitute your expression for E and integrate to get Delta V. Which conductor is at the higher potential? Finally obtain your expression for capacitance per unit length. Check that it depends only on the dimensions of the cable and epsilon 0 (multiplied by a dielectric constant if there is an insulating material between the conductors) What is the capacitance of a 50 m long cable with a = 1mm and b = 3mm, filled with a nylon dielectric of dielectric constant 3.5?
shakti8630Lv7
24 Jan 2023