On a dry day, your body can accumulate static charge from walking across a carpet or from brushing your hair. If your body develops a charge of -15 µC (microcoulombs), what is their collective mass?

검증된 단계별 안내

Identify the charge given in the problem, which is -15 mC (microcoulombs). Note that 1 microcoulomb (mC) equals \(1 imes 10^{-6}\) coulombs (C).

Recognize that the charge carriers in the human body are primarily electrons. The charge of one electron is approximately \(-1.602 imes 10^{-19}\) coulombs.

Calculate the number of electrons corresponding to a total charge of -15 mC. Use the formula: Number of electrons = Total charge / Charge of one electron.

Determine the mass of one electron, which is approximately \(9.109 imes 10^{-31}\) kilograms.

Calculate the total mass of the electrons by multiplying the number of electrons by the mass of one electron.

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주요 개념

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Coulomb's Law

Coulomb's Law describes the electrostatic force between charged objects. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is fundamental in understanding how static charges interact, which is relevant when considering the accumulation of charge on the body.

Charge and Mass Relationship

The relationship between charge and mass can be explored through the concept of charge-to-mass ratio. While charge itself does not have mass, the energy associated with a charge can be related to mass via Einstein's equation, E=mc². This concept is crucial for calculating the effective mass of a charged object based on its electric potential energy.

Microcoulombs to Mass Conversion

To find the mass associated with a given charge, one can use the energy stored in the electric field created by the charge. The conversion involves calculating the energy using the charge and potential difference, then applying the mass-energy equivalence principle. This process allows for the determination of the mass equivalent of the static charge accumulated on the body.