An electric dipole consists of two opposite charges each `0.05 mu C` separated by 30 mm. The dipole is placed in an uniform external electric field of `10^(6)NC^(-1)`. The maximum torque exerted by the field on the dipole is

Options

A. `6 xx 10^(3) Nm`
B. `3 xx 10^(-3)Nm`
C. `15 xx 10^(-3)Nm`
D. `1.5 xx 10^(-3)Nm`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given values
We have:
- Charge of each dipole, \( q = 0.05 \, \mu C = 0.05 \times 10^{-6} \, C \)
- Separation between the charges, \( d = 30 \, mm = 30 \times 10^{-3} \, m \)
- External electric field, \( E = 10^6 \, N/C \)

### Step 2: Calculate the dipole moment \( p \)
The dipole moment \( p \) is given by the formula:
\[ p = q \cdot d \]
Substituting the values:
\[ p = (0.05 \times 10^{-6} \, C) \cdot (30 \times 10^{-3} \, m) \]
Calculating this:
\[ p = 0.05 \times 30 \times 10^{-9} \, C \cdot m = 1.5 \times 10^{-6} \, C \cdot m \]

### Step 3: Use the formula for torque \( \tau \)
The torque \( \tau \) on a dipole in an electric field is given by:
\[ \tau = p \cdot E \cdot \sin(\theta) \]
For maximum torque, \( \sin(\theta) \) should be 1, which occurs when \( \theta = 90^\circ \):
\[ \tau_{max} = p \cdot E \]

### Step 4: Substitute the values to find maximum torque
Substituting the values of \( p \) and \( E \):
\[ \tau_{max} = (1.5 \times 10^{-6} \, C \cdot m) \cdot (10^6 \, N/C) \]
Calculating this:
\[ \tau_{max} = 1.5 \times 10^{-6} \times 10^6 \, N \cdot m = 1.5 \, N \cdot m \]

### Final Answer
The maximum torque exerted by the field on the dipole is:
\[ \tau_{max} = 1.5 \, N \cdot m \]

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