For a dipole `q= 2xx10^(-6)C` and `d= 0.01m`. Calculate the maximum torque for this dipole if `E= 5xx10^(5)N//C`

Options

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

Answer

To solve the problem of calculating the maximum torque for a dipole, we can follow these steps:

### Step 1: Calculate the Dipole Moment (P)
The dipole moment \( P \) is given by the formula:
\[ P = q \cdot d \]
where:
- \( q = 2 \times 10^{-6} \, \text{C} \) (charge)
- \( d = 0.01 \, \text{m} \) (distance between the charges)

Substituting the values:
\[ P = 2 \times 10^{-6} \, \text{C} \times 0.01 \, \text{m} = 2 \times 10^{-8} \, \text{C m} \]

### Step 2: Use the Torque Formula
The torque \( \tau \) experienced by a dipole in an electric field is given by the formula:
\[ \tau = P \cdot E \cdot \sin(\theta) \]
where:
- \( E = 5 \times 10^{5} \, \text{N/C} \) (electric field)
- \( \theta \) is the angle between the dipole moment and the electric field.

### Step 3: Calculate Maximum Torque
The maximum torque occurs when \( \sin(\theta) = 1 \), which corresponds to \( \theta = 90^\circ \). Therefore, the maximum torque \( \tau_{\text{max}} \) is:
\[ \tau_{\text{max}} = P \cdot E \]

Substituting the values we calculated:
\[ \tau_{\text{max}} = (2 \times 10^{-8} \, \text{C m}) \cdot (5 \times 10^{5} \, \text{N/C}) \]

Calculating this gives:
\[ \tau_{\text{max}} = 10 \times 10^{-3} \, \text{N m} = 1 \times 10^{-2} \, \text{N m} \]

### Final Answer
Thus, the maximum torque for the dipole is:
\[ \tau_{\text{max}} = 10 \times 10^{-3} \, \text{N m} \]