Electricity and Magnetism

Capacitors and Transformers

Gauss' law to find capacitance

         

The concentric plates of a spherical capacitor have radii a=4.1 mma=4.1\text{ mm} and b=4.6 mm.b=4.6\text{ mm}. The above diagram shows the cross sectional feature of the capacitor. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is ε0=8.85×1012 F/m.\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.

What is the approximate capacitance of a copper sphere with a radius of 2.50 mm?2.50\text{ mm}?

The value of the permittivity constant is ε0=8.85×1012 F/m.\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.

A cylindrical capacitor has radii a=1.1 mma=1.1\text{ mm} and b=2.9 mmb=2.9\text{ mm} and length L=6.0 cm,L=6.0\text{ cm}, as shown in the above cross sectional feature of the capacitor. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is ε0=8.85×1012 F/m.\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.

Suppose that 44 identical mercury spheres with radius R=1.20 mmR=1.20\text{ mm} are merged to one sphere. What is the approximate capacitance of the merged mercury drop?

The value of the permittivity constant is ε0=8.85×1012 F/m.\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.

A parallel-plate capacitor has 58.0 cm258.0\text{ cm}^2 of plate area and 1.20 mm1.20\text{ mm} separation. What is the approximate capacitance of the capacitor?

The value of the permittivity constant is ε0=8.85×1012 F/m.\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.

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