A parallel-plate capacitor has capacitance C0=5.00 pF when there is air between the plates. The

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A parallel-plate capacitor has capacitance C0=5.00 pF when...

A parallel-plate capacitor has capacitance $C_{0}=5.00 \mathrm{pF}$ when there is air between the plates. The separation between the plates is 1.50 $\mathrm{mm}$ (a) What is the maximum magnitude of charge $Q$ that can be placed on each plate if the electric field in the region between the plates is not to exceed $3.00 \times 10^{4} \mathrm{V} / \mathrm{m}$ (b) A dielectric with $K=2.70$ is inserted between the plates of the capacitor, completely filling the volume between the plates. Now what is the maximum magnitude of charge on each plate if the electric field between the plates is not to exceed $3.00 \times 10^{4} \mathrm{V} / \mathrm{m}$ ?

A parallel-plate capacitor has capacitance $C_{0}=5.00 \mathrm{pF}$ when there is air between the plates. The separation between the plates is 1.50 $\mathrm{mm}$ (a) What is the maximum magnitude of charge $Q$ that can be placed on each plate if the electric field in the region between the plates is not to exceed $3.00 \times 10^{4} \mathrm{V} / \mathrm{m}$ (b) A dielectric with $K=2.70$ is inserted between the plates of the capacitor, completely filling the volume between the plates. Now what is the
maximum magnitude of charge on each plate if the electric field between the plates is not to exceed $3.00 \times 10^{4} \mathrm{V} / \mathrm{m}$ ?

Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor is a device consisting of two conductive plates separated by a dielectric medium. Its capacitance depends on the area of the plates, the distance between them, and the permittivity of the dielectric medium. This concept is fundamental in understanding how energy is stored in the electric field between the plates.

Electric Field and Voltage Relationship

The electric field between the plates of a capacitor is directly related to the voltage across the plates and inversely related to the distance between them, given by E = V/d. This relationship allows one to determine the potential difference from the known field strength and plate separation, which is essential when imposing limits to prevent dielectric breakdown.

Dielectric

A dielectric is an insulating material inserted between the plates of a capacitor to increase its capacitance by reducing the effective electric field. The dielectric constant (or relative permittivity) quantifies this effect by indicating how much the material increases the capacitance compared to a vacuum. Understanding this concept is critical when modifying capacitor properties for specific applications.

Capacitance and Maximum Charge

The relationship Q = CV links the charge stored on a capacitor to its capacitance and the applied voltage. When there is a limit on the maximum allowable electric field, this relationship is used alongside the electric field-voltage equation to determine the maximum charge that can be safely stored. This synthesis of concepts ensures that capacitors are operated within their safe electrical limits.

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