An electric dipole consists of two opposite charges of magnitude `1muC` separated by a distance of `2cm`.The dipole is placed in an electric filled `10^(-5)Vm^(-1)`.The maximum torque that the field exert on the dipole is

Options

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

Answer

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

### Step 1: Understand the Given Data
- The charge of the dipole, \( q = 1 \mu C = 1 \times 10^{-6} C \)
- The separation distance between the charges, \( d = 2 cm = 2 \times 10^{-2} m \)
- The electric field strength, \( E = 10^{-5} V/m \)

### Step 2: Calculate the Dipole Moment
The dipole moment \( p \) is given by the formula:
\[ p = q \cdot d \]
Substituting the values:
\[ p = (1 \times 10^{-6} C) \cdot (2 \times 10^{-2} m) = 2 \times 10^{-8} C \cdot m \]

### Step 3: Determine the Maximum Torque
The maximum torque \( \tau_{max} \) on a dipole in an electric field is given by:
\[ \tau_{max} = p \cdot E \]
Substituting the values we have:
\[ \tau_{max} = (2 \times 10^{-8} C \cdot m) \cdot (10^{-5} V/m) \]

### Step 4: Perform the Calculation
Calculating the maximum torque:
\[ \tau_{max} = 2 \times 10^{-8} \cdot 10^{-5} = 2 \times 10^{-13} N \cdot m \]

### Final Answer
The maximum torque that the electric field exerts on the dipole is:
\[ \tau_{max} = 2 \times 10^{-13} N \cdot m \]

---