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Electricity and Magnetism

Capacitors and Transformers

Gauss' law to find capacitance

         

The concentric plates of a spherical capacitor have radii \(a=4.1\text{ mm}\) and \(b=4.6\text{ mm}.\) 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 \(\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.\)

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

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

A cylindrical capacitor has radii \(a=1.1\text{ mm}\) and \(b=2.9\text{ mm}\) and length \(L=6.0\text{ cm},\) 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 \(\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.\)

Suppose that \(4\) identical mercury spheres with radius \(R=1.20\text{ mm}\) are merged to one sphere. What is the approximate capacitance of the merged mercury drop?

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

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

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

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