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 -22 mC (microcoulombs), what is their collective mass?

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Understand that the problem involves finding the mass of electrons corresponding to a given charge.

Recall that the charge of a single electron is approximately \(-1.602 \times 10^{-19}\) coulombs.

Calculate the number of electrons by dividing the total charge by the charge of a single electron: \(\text{Number of electrons} = \frac{-22 \times 10^{-6} \text{ C}}{-1.602 \times 10^{-19} \text{ C/electron}}\).

Use the mass of a single electron, which is approximately \(9.109 \times 10^{-31}\) kg, to find the total mass: \(\text{Mass} = \text{Number of electrons} \times 9.109 \times 10^{-31} \text{ kg/electron}\).

Perform the calculations to find the collective mass of the electrons.

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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 and can help explain the accumulation of charge on the body.

Charge and Mass Relationship

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

Microcoulombs to Mass Conversion

To find the mass associated with a given charge, one can use the concept of energy stored in an electric field. The energy (E) can be related to charge (Q) and voltage (V) through the equation E = QV. By knowing the voltage and using the relationship between energy and mass, one can convert the charge in microcoulombs to an equivalent mass, which is essential for solving the problem.