The maximum amount of charge that can be collected on a Van...

The maximum amount of charge that can be collected on a Van de Graaff generator's conducting sphere (30-cm diameter) is about $30 \mu \mathrm{C}$. Calculate the surface charge density, $\sigma$, of the sphere in $\mathrm{C} / \mathrm{m}^{2}$

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Key Concepts

Surface Charge Density

This is a measure of how much electric charge is distributed over a unit area. In this context, it is defined for a conductor, where the charge spreads uniformly over the surface. The calculation involves dividing the total charge by the total surface area of the sphere, making it a fundamental concept in electrostatics.

Surface Area of a Sphere

To compute the surface charge density on a spherical conductor, it's necessary to know the formula for the surface area of a sphere. The surface area is calculated as 4?r², where r is the radius of the sphere. This concept is crucial in determining how the total charge is distributed over the curved surface.

Electric Charge

Electric charge is a basic property of matter that causes it to experience a force when placed in an electromagnetic field. In problems like this, the total charge (given as 30 ?C) must be understood and converted to standard units if necessary, serving as the numerator in the surface charge density formula.

Unit Conversion

Unit conversion is an essential procedure in physics to ensure consistency in calculations. For example, converting microcoulombs to coulombs is necessary so that all measurements are in standard SI units when applying equations such as the one for surface charge density.

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