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Two coaxial tubes are inserted into a tray containing an insulating liquid (oil) with a dielectric constant of , and a mass density of Pm [kg/m³]. A voltage Vo is applied between the tubes as shown, and this causes the level of the oil to rise to a level h in the space between the tubes due to electrostatic forces. Recall that the capacitance per unit length of a coaxial structure is given by [F/m] C= 2πε In(b/a) h air Eo oil Er where a and b are the inner and outer radii of the coaxial structure, respectively. (a) First find the capacitance of the structure as shown. (b) Next find the force acting on the dielectric (oil) (c) Find the height h to which the oil rises in the tube as a function of V.

Two coaxial tubes are inserted into a tray containing an insulating liquid (oil) with a dielectric constant of , and a mass density of Pm [kg/m³]. A voltage Vo is applied between the tubes as shown, and this causes the level of the oil to rise to a level h in the space between the tubes due to electrostatic forces. Recall that the capacitance per unit length of a coaxial structure is given by [F/m] C= 2πε In(b/a) h air Eo oil Er where a and b are the inner and outer radii of the coaxial structure, respectively. (a) First find the capacitance of the structure as shown. (b) Next find the force acting on the dielectric (oil) (c) Find the height h to which the oil rises in the tube as a function of V.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Two coaxial tubes are inserted into a tray containing an insulating liquid (oil) with a dielectric constant of \( \varepsilon_r \), and a mass density of \( \rho_m \) [kg/m\(^3\)]. A voltage \( V_0 \) is applied between the tubes as shown, and this causes the level of the oil to rise to a level \( h \) in the space between the tubes due to electrostatic forces. Recall that the capacitance **per unit length** of a coaxial structure is given by \[ C = \frac{2 \pi \varepsilon}{\ln(b/a)} \quad [\text{F/m}] \] where \( a \) and \( b \) are the inner and outer radii of the coaxial structure, respectively. (a) First find the capacitance of the structure as shown. (b) Next find the force acting on the dielectric (oil). (c) Find the height \( h \) to which the oil rises in the tube as a function of \( V_0 \). **Diagram Explanation:** The diagram shows two concentric cylinders (coaxial tubes) with an insulating liquid (oil) between them. The inner cylinder is surrounded by air with permittivity \( \varepsilon_0 \) and the space between the cylinders is filled with oil with permittivity \( \varepsilon_r \). The voltage applied is \( V_0 \), and this setup causes the liquid to rise to height \( h \). The length of the tubes is \( \ell \).
Transcribed Image Text:Two coaxial tubes are inserted into a tray containing an insulating liquid (oil) with a dielectric constant of \( \varepsilon_r \), and a mass density of \( \rho_m \) [kg/m\(^3\)]. A voltage \( V_0 \) is applied between the tubes as shown, and this causes the level of the oil to rise to a level \( h \) in the space between the tubes due to electrostatic forces. Recall that the capacitance **per unit length** of a coaxial structure is given by \[ C = \frac{2 \pi \varepsilon}{\ln(b/a)} \quad [\text{F/m}] \] where \( a \) and \( b \) are the inner and outer radii of the coaxial structure, respectively. (a) First find the capacitance of the structure as shown. (b) Next find the force acting on the dielectric (oil). (c) Find the height \( h \) to which the oil rises in the tube as a function of \( V_0 \). **Diagram Explanation:** The diagram shows two concentric cylinders (coaxial tubes) with an insulating liquid (oil) between them. The inner cylinder is surrounded by air with permittivity \( \varepsilon_0 \) and the space between the cylinders is filled with oil with permittivity \( \varepsilon_r \). The voltage applied is \( V_0 \), and this setup causes the liquid to rise to height \( h \). The length of the tubes is \( \ell \).
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The capacitance, C=2πε∘lnba F/m

The given diagram is shown below,

Electrical Engineering homework question answer, step 1, image 1

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