If 8 field lines come out of + 1 C charge, how many field lines will end at -2C charge?

Options

A. 0
B. 8
C. 16
D. 32

Explanation

To solve the problem of how many electric field lines will end at a -2 C charge given that 8 field lines come out of a +1 C charge, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: Electric field lines are directly proportional to the magnitude of the charge. This means that if we know the number of field lines for one charge, we can calculate it for another charge using their magnitudes.

2. **Identify Given Values**:
- Charge \( Q_1 = +1 \, \text{C} \)
- Number of field lines from \( Q_1 \) (denoted as \( L_1 \)) = 8
- Charge \( Q_2 = -2 \, \text{C} \) (we only consider the magnitude, which is 2 C)

3. **Set Up the Proportionality**: Since the number of field lines is proportional to the magnitude of the charge, we can express this relationship mathematically:
\[ \frac{L_1}{L_2} = \frac{Q_1}{Q_2} \]
where \( L_2 \) is the number of field lines ending at the -2 C charge.

4. **Substitute Known Values**:
\[ \frac{8}{L_2} = \frac{1}{2} \]

5. **Cross-Multiply to Solve for \( L_2 \)**:
\[ 8 \cdot 2 = 1 \cdot L_2 \]
\[ L_2 = 16 \]

6. **Conclusion**: Therefore, the number of field lines that will end at the -2 C charge is 16.

### Final Answer:
The number of field lines that will end at the -2 C charge is **16**.