An uniform electric field of magnitude `5 xx 10^(4) NC^(-1)` has a dipole of dipole moment `4xx 10^(-9) cm` aligned at `30^(@)` with the direction of field. Calculate the magnitude of torque acting on the dipole:

Options

A. `10^(-4)Nm`
B. `2xx10^(-3)Nm`
C. `2xx10^(-5)Nm`
D. `10^(-5)Nm`

Explanation

To solve the problem, we need to calculate the torque (\( \tau \)) acting on a dipole in a uniform electric field. The formula for the torque on a dipole in an electric field is given by:

\[ \tau = P \cdot E \cdot \sin(\theta) \]

where:
- \( P \) is the dipole moment,
- \( E \) is the electric field strength,
- \( \theta \) is the angle between the dipole moment and the electric field.

### Step-by-step Solution:

1. **Identify the given values**:
- Electric field, \( E = 5 \times 10^4 \, \text{N/C} \)
- Dipole moment, \( P = 4 \times 10^{-9} \, \text{C m} \)
- Angle, \( \theta = 30^\circ \)

2. **Convert the angle to radians (if necessary)**:
- In this case, we can use \( \sin(30^\circ) \) directly, which is \( \frac{1}{2} \).

3. **Substitute the values into the torque formula**:
\[ \tau = P \cdot E \cdot \sin(\theta) \]
\[ \tau = (4 \times 10^{-9} \, \text{C m}) \cdot (5 \times 10^4 \, \text{N/C}) \cdot \sin(30^\circ) \]

4. **Calculate \( \sin(30^\circ) \)**:
\[ \sin(30^\circ) = \frac{1}{2} \]

5. **Plug in the value of \( \sin(30^\circ) \)**:
\[ \tau = (4 \times 10^{-9}) \cdot (5 \times 10^4) \cdot \left(\frac{1}{2}\right) \]

6. **Perform the multiplication**:
\[ \tau = (4 \times 5 \times \frac{1}{2}) \times 10^{-9} \times 10^4 \]
\[ = (10) \times 10^{-9 + 4} \]
\[ = 10 \times 10^{-5} \, \text{N m} \]
\[ = 10^{-4} \, \text{N m} \]

7. **Final Result**:
\[ \tau = 1 \times 10^{-4} \, \text{N m} \]

### Conclusion:
The magnitude of the torque acting on the dipole is \( 1 \times 10^{-4} \, \text{N m} \).