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

Options

A. `12 xx 10^(-1) N-m`
B. `12 xx 10^(-2)N-m`
C. `12 xx 10^(-3) N-m`
D. `12 xx 10^(-4) N-m`

Answer

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

### Step 1: Identify the given values
- Charge of each dipole, \( q = 2 \times 10^{-6} \, C \)
- Distance between the charges, \( d = 3 \, cm = 3 \times 10^{-2} \, m \)
- Electric field strength, \( E = 2 \times 10^{5} \, N/C \)

### Step 2: Calculate the dipole moment \( p \)
The dipole moment \( p \) is given by the formula:
\[ p = q \times d \]
Substituting the values:
\[ p = (2 \times 10^{-6} \, C) \times (3 \times 10^{-2} \, m) = 6 \times 10^{-8} \, C \cdot m \]

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

### Step 4: Perform the multiplication
Calculating the above expression:
\[ \tau_{max} = 12 \times 10^{-3} \, N \cdot m = 1.2 \times 10^{-2} \, N \cdot m \]

### Step 5: Write the final answer
The maximum torque on the dipole is:
\[ \tau_{max} = 1.2 \times 10^{-2} \, N \cdot m \]