A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. How many charged particles were transferred?

검증된 단계별 안내

Determine the change in charge on the plastic rod. The initial charge on the rod is \(-15 \; \text{nC}\), and the final charge is \(-10 \; \text{nC}\). The change in charge is given by \(\Delta Q = Q_{\text{final}} - Q_{\text{initial}}\).

Substitute the values into the formula: \(\Delta Q = -10 \; \text{nC} - (-15 \; \text{nC})\). Simplify the expression to find the total charge transferred.

Recall that the charge of a single electron is \(e = -1.6 \times 10^{-19} \; \text{C}\). The number of charged particles (electrons) transferred can be calculated using the formula \(n = \frac{\Delta Q}{e}\), where \(n\) is the number of electrons.

Substitute the value of \(\Delta Q\) (calculated in step 2) and \(e = -1.6 \times 10^{-19} \; \text{C}\) into the formula \(n = \frac{\Delta Q}{e}\).

Simplify the expression to find the number of electrons transferred. Note that the result should be a positive value, as the number of particles is always positive.

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주요 개념

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Charge Conservation

Charge conservation is a fundamental principle in physics stating that the total electric charge in an isolated system remains constant over time. When two objects come into contact, charge can be transferred between them, but the sum of their charges before and after the interaction must remain the same. This principle is crucial for understanding how charges redistribute when conductive materials interact.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law helps explain how charged particles interact and can be used to calculate the forces involved when charges are transferred between objects.

Elementary Charge

The elementary charge is the smallest unit of electric charge, denoted as 'e', approximately equal to 1.6 x 10^-19 coulombs. It is the charge carried by a single proton or the negative of that carried by a single electron. Understanding the elementary charge is essential for calculating the number of charged particles transferred during interactions, as charges are quantized and always occur in integer multiples of this fundamental charge.