If an object contains `n_1`, protons and `n_2` electrons the net charge on the object is

Options

A. `(n_1+n_2)e`
B. `(n_1-n_2)e`
C. `(n_2-n_1)e`
D. Zero

Answer

To find the net charge on an object that contains \( n_1 \) protons and \( n_2 \) electrons, we can follow these steps:

### Step 1: Understand the charges of protons and electrons
- Protons have a positive charge denoted as \( +e \).
- Electrons have a negative charge denoted as \( -e \).

### Step 2: Write the expression for the total charge
The total charge \( Q \) on the object can be calculated by considering the contributions from both protons and electrons:
\[ Q = (n_1 \times \text{charge of a proton}) + (n_2 \times \text{charge of an electron}) \]
Substituting the values of the charges:
\[ Q = (n_1 \times e) + (n_2 \times (-e)) \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ Q = n_1 \times e - n_2 \times e \]
Factoring out \( e \):
\[ Q = e(n_1 - n_2) \]

### Step 4: Interpret the result
The net charge \( Q \) on the object is given by:
\[ Q = e(n_1 - n_2) \]
Where:
- \( n_1 \) is the number of protons,
- \( n_2 \) is the number of electrons,
- \( e \) is the elementary charge (approximately \( 1.6 \times 10^{-19} \) coulombs).

### Final Answer
Thus, the net charge on the object is:
\[ Q = e(n_1 - n_2) \]

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