The charge center of a thundercloud, drifting 3.0 km above...

The charge center of a thundercloud, drifting 3.0 km above the earth's surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and modeling the charge center and the earth's surface as parallel plates, calculate: (a) the capacitance of the system; (b) the potential difference between charge center and ground; (c) the average strength of the electric field between cloud and ground; (d) the electrical energy stored in the system.

Key Concepts

Stored Electrical Energy

The energy stored in a capacitor is defined by the formula U = ½CV² or equivalently U = ½Q²/C. This energy represents the work done to assemble the charge distribution against the electric field and is an important concept in both theoretical and applied aspects of electrostatics and energy storage devices.

Electric Field in a Capacitor

In a parallel plate capacitor, the electric field is typically uniform and is directly related to the voltage across the plates divided by the separation distance, given by E = V/d. This concept is crucial for understanding how the applied voltage creates an electric field that influences the behavior of charges within the system.

Capacitance of a Parallel Plate System

Capacitance measures the ability of a system to store electrical charge per unit voltage. In a parallel plate configuration, capacitance is determined by the area of the plates and the distance between them, typically using the formula C = ??A/d, where ?? is the electric constant. This concept is fundamental in understanding how geometric factors influence charge storage in capacitors.

Voltage-Charge Relationship

The relationship between voltage (potential difference) and charge in a capacitor is expressed by V = Q/C, where Q is the charge stored and C is the capacitance. This principle connects how much charge is stored to the electrical potential difference, providing a basis for analyzing and designing systems that involve energy storage and transfer.

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