×
Electricity and Magnetism

# 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 $$\varepsilon_0=8.85 \times 10^{-12} \text{ F/m}.$$

×