Question

A conductor has positive charge of \(2.4 \times 10^{-18}\) coulomb. Find how much electrons are in deficit/excess on the conductor.

Hint:

Remember the sign convention: A positive net charge means an object has lost electrons (deficit). A negative net charge means an object has gained electrons (excess).

Answer 1

Step 1: Understanding the Concept:
The charge on any object is an integer multiple of the elementary charge (the charge of a single electron). This is the principle of quantization of charge. A positive charge on a conductor indicates a removal of electrons, leading to a deficit.
Step 2: Key Formula or Approach:
The formula for quantization of charge is:
\[ Q = ne \] where: Q is the total charge on the object.
n is the number of electrons in excess or deficit (must be an integer).
e is the magnitude of the elementary charge, \( e = 1.6 \times 10^{-19} \) C.
We need to solve for n.
Step 3: Detailed Explanation:
We are given:
Total charge \( Q = +2.4 \times 10^{-18} \) C.
Elementary charge \( e = 1.6 \times 10^{-19} \) C.
Rearranging the formula to solve for n: \[ n = \frac{Q}{e} \] Substituting the values: \[ n = \frac{2.4 \times 10^{-18}}{1.6 \times 10^{-19}} \] \[ n = \frac{2.4}{1.6} \times 10^{-18 - (-19)} = \frac{24}{16} \times 10^{1} = 1.5 \times 10 = 15 \] Since the charge Q is positive, it means that electrons (which are negatively charged) have been removed from the conductor. Therefore, there is a deficit of 15 electrons.
Step 4: Final Answer:
The conductor has a deficit of 15 electrons.