The electric charges of +9C, -10C and -8C are enclosed anywhere by a closed surface. T.N.E.I. through that surface is

Options

A. `-9 C`
B. `+9 C`
C. `5 C`
D. `4 C`

Explanation

To solve the problem of finding the Total Normal Electric Induction (T.N.E.I.) through a closed surface that encloses charges of +9C, -10C, and -8C, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges**:
We have three charges:
- \( Q_1 = +9 \, \text{C} \)
- \( Q_2 = -10 \, \text{C} \)
- \( Q_3 = -8 \, \text{C} \)

2. **Calculate the Total Charge Enclosed**:
To find the total charge enclosed by the surface, we sum the individual charges:
\[ Q_{\text{enclosed}} = Q_1 + Q_2 + Q_3 \]
Substituting the values:
\[ Q_{\text{enclosed}} = 9 + (-10) + (-8) \]

3. **Perform the Calculation**:
Simplifying the expression:
\[ Q_{\text{enclosed}} = 9 - 10 - 8 \]
\[ Q_{\text{enclosed}} = 9 - 18 = -9 \, \text{C} \]

4. **Relate Total Normal Electric Induction to Enclosed Charge**:
According to Gauss's law, the Total Normal Electric Induction (T.N.E.I.) through a closed surface is directly proportional to the total charge enclosed:
\[ \text{T.N.E.I.} = Q_{\text{enclosed}} = -9 \, \text{C} \]

5. **Conclusion**:
Therefore, the Total Normal Electric Induction (T.N.E.I.) through the closed surface is:
\[ \text{T.N.E.I.} = -9 \, \text{C} \]

### Final Answer:
The Total Normal Electric Induction (T.N.E.I.) through the closed surface is \(-9 \, \text{C}\).

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