An electric dipole consisting of two opposite charges of `2xx10^(-6)C` each separated by a distance of `3 cm` is placed in an electric field of `2xx10^(5)N//C`. The maximum torque on the dipole will be

Options

A. `12xx10^(-1)Nm`
B. `12xx10^(-3)Nm`
C. `24xx10^(-1)Nm`
D. `24xx10^(-3)Nm`

Explanation

To find the maximum torque on an electric dipole placed in an electric field, we can follow these steps:

### Step 1: Understand the parameters of the dipole
We have:
- Charge \( q = 2 \times 10^{-6} \, C \)
- Separation distance \( d = 3 \, cm = 0.03 \, m \)
- Electric field \( E = 2 \times 10^{5} \, N/C \)

### Step 2: Calculate the dipole moment \( p \)
The dipole moment \( p \) is given by the formula:
\[ p = q \cdot d \]
Substituting the values:
\[ p = (2 \times 10^{-6} \, C) \cdot (0.03 \, m) = 6 \times 10^{-8} \, C \cdot m \]

### Step 3: Use the formula for maximum torque
The maximum torque \( \tau \) on an electric dipole in an electric field is given by:
\[ \tau_{\text{max}} = E \cdot p \]
Substituting the values of \( E \) and \( p \):
\[ \tau_{\text{max}} = (2 \times 10^{5} \, N/C) \cdot (6 \times 10^{-8} \, C \cdot m) \]

### Step 4: Perform the calculation
Calculating the torque:
\[ \tau_{\text{max}} = 2 \times 6 \times 10^{5} \times 10^{-8} = 12 \times 10^{-3} \, N \cdot m \]
Thus,
\[ \tau_{\text{max}} = 0.012 \, N \cdot m \]

### Conclusion
The maximum torque on the dipole is \( 0.012 \, N \cdot m \).

---