An electric dipole consists of two charges of `0.1muC` separated bu a distance of `2.0cm`. The dipole is placed in an external field of `10^(5)NC^(-1)`. What maximum torqur does the field exert on the dipole?

Options

A. `4xx10^(-4) Nm`
B. `5xx10^(-4) Nm`
C. `8xx10^(-4) Nm`
D. `2xx10^(-4) Nm`

Explanation

To solve the problem of finding the maximum torque exerted on an electric dipole in an external electric field, we can follow these steps:

### Step 1: Understand the Given Information
We have:
- Charge of each dipole, \( q = 0.1 \, \mu C = 0.1 \times 10^{-6} \, C \)
- Separation distance, \( d = 2.0 \, cm = 2.0 \times 10^{-2} \, m \)
- External electric field, \( E = 10^5 \, N/C \)

### Step 2: Calculate the Dipole Moment (P)
The dipole moment \( P \) is given by the formula:
\[ P = q \cdot d \]
Substituting the values:
\[ P = (0.1 \times 10^{-6} \, C) \cdot (2.0 \times 10^{-2} \, m) = 0.1 \times 2.0 \times 10^{-8} \, C \cdot m = 2.0 \times 10^{-8} \, C \cdot m \]

### Step 3: Determine the Maximum Torque (τ)
The torque \( \tau \) on a dipole in an electric field is given by:
\[ \tau = P \cdot E \cdot \sin(\theta) \]
The maximum torque occurs when \( \sin(\theta) = 1 \) (i.e., when \( \theta = 90^\circ \)):
\[ \tau_{\text{max}} = P \cdot E \]
Substituting the values:
\[ \tau_{\text{max}} = (2.0 \times 10^{-8} \, C \cdot m) \cdot (10^5 \, N/C) \]
\[ \tau_{\text{max}} = 2.0 \times 10^{-3} \, N \cdot m \]

### Step 4: Final Result
The maximum torque exerted on the dipole by the external electric field is:
\[ \tau_{\text{max}} = 2.0 \times 10^{-3} \, N \cdot m \]