(II) A manufacturer claims that a carpet will not generate more than 5.0 kV of static electricit

step 1 We have static electricity between some slippers and a carpet. We're told that the maximum volta

(II) A manufacturer claims that a carpet will not generate...

(II) A manufacturer claims that a carpet will not generate more than 5.0 $\mathrm{kV}$ of static electricity. What magnitude of charge would have to be transferred between a carpet and a shoe for there to be a $5.0-\mathrm{kV}$ potential difference between the shoe and the carpet. Approximate the shoe and the carpet as large sheets of charge separated by a distance $d=1.0 \mathrm{mm}.$

Key Concepts

Capacitance

Capacitance is a measure of a system's ability to store charge per unit potential difference. It depends on the geometry and the medium between conductive elements and is given by relationships such as C = ??A/d for parallel plate configurations, where ?? is the permittivity of free space, A is the area of the plates, and d is the separation between them.

Parallel Plate Capacitor Approximation

The parallel plate capacitor model simplifies the analysis of systems where two conductive surfaces are separated by a small distance. This approximation assumes a uniform electric field between the plates and provides a basis for understanding the relationship between charge, voltage, and capacitance in many practical electrostatic problems.

Electric Potential Difference

Electric potential difference, often simply called voltage, represents the work needed to move a unit charge from one point to another against an electric field. In capacitor configurations, it is directly related to the amount of charge stored and the capacitance of the system, as encapsulated by the relation V = Q/C.

Static Electricity

Static electricity involves the accumulation of electric charge on surfaces, often resulting from the transfer of electrons between materials. This buildup can generate significant electrical potentials, which are important in understanding phenomena such as the generation of a measurable voltage difference between objects.

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