A piece of Styrofoam having a mass m carries a net charge of...

A piece of Styrofoam having a mass $m$ carries a net charge of $-q$ and floats above the center of a very large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?

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Key Concepts

Mechanical Equilibrium

Mechanical equilibrium occurs when the net force acting on an object equals zero, ensuring that the object remains at rest or moves with constant velocity. In situations involving charged objects in an electric field, equilibrium is achieved when the electric force balances other forces such as gravity.

Uniformly Charged Plane

An infinite or very large plane uniformly charged with a surface charge density produces an electric field whose magnitude is constant and given by the formula E = ?/(2??). This result, derived from Gauss's law, is notable because the field does not depend on the distance from the plane, which simplifies many electrostatic problems.

Electric Force on a Charge

A charged object in an electric field experiences a force described by F = qE, where q represents the charge on the object and E is the electric field. The direction of the force depends on the sign of the charge; a positive charge is accelerated in the direction of the field while a negative charge moves opposite to it.

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