How many electrons would have to be removed from a copper penny to leave it with a positive charge of `10^(-7) C` ?

Answer

To determine how many electrons need to be removed from a copper penny to leave it with a positive charge of \(10^{-7} \, C\), we can follow these steps:

### Step 1: Understand the relationship between charge and number of electrons
The charge \(Q\) of an object is related to the number of electrons \(N\) removed (or added) and the charge of a single electron \(e\) by the formula:
\[ Q = N \cdot e \]
Where:
- \(Q\) is the total charge (in coulombs),
- \(N\) is the number of electrons,
- \(e\) is the charge of a single electron, approximately \(1.6 \times 10^{-19} \, C\).

### Step 2: Rearrange the formula to solve for \(N\)
To find the number of electrons \(N\) that need to be removed, we can rearrange the formula:
\[ N = \frac{Q}{e} \]

### Step 3: Substitute the known values
We know:
- \(Q = 10^{-7} \, C\)
- \(e = 1.6 \times 10^{-19} \, C\)

Substituting these values into the equation gives:
\[ N = \frac{10^{-7}}{1.6 \times 10^{-19}} \]

### Step 4: Perform the calculation
Now we can perform the division:
\[ N = \frac{10^{-7}}{1.6 \times 10^{-19}} = \frac{10^{-7}}{1.6} \times 10^{19} \]

Calculating \( \frac{10^{-7}}{1.6} \):
\[ \frac{10^{-7}}{1.6} \approx 0.625 \times 10^{12} = 6.25 \times 10^{11} \]

### Step 5: Conclusion
Thus, the number of electrons that need to be removed from the copper penny to leave it with a positive charge of \(10^{-7} \, C\) is:
\[ N \approx 6.25 \times 10^{11} \]

### Final Answer:
**Approximately \(6.25 \times 10^{11}\) electrons need to be removed.**

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