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. `1xx10^(-3)Nm^(-1)`
B. `10xx10^(-3)Nm^(-1)`
C. `10xx10^(-3)Nm`
D. `1xx10^(2)Nm^(2)`

Explanation

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

### Step 1: Understand the formula for torque
The maximum torque (\( \tau \)) experienced by a dipole in an electric field is given by the formula:
\[ \tau = E \cdot P \]
where:
- \( E \) is the electric field strength,
- \( P \) is the dipole moment.

### Step 2: Calculate the dipole moment
The dipole moment (\( P \)) is calculated using the formula:
\[ P = q \cdot d \]
where:
- \( q \) is the charge,
- \( d \) is the distance between the charges.

Given:
- \( q = 2 \times 10^{-6} \, \text{C} \)
- \( d = 0.01 \, \text{m} \)

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

### Step 3: Substitute values into the torque formula
Now, we substitute the values of \( E \) and \( P \) into the torque formula:
- Given \( E = 5 \times 10^{5} \, \text{N/C} \)

Calculating the torque:
\[ \tau = E \cdot P = (5 \times 10^{5} \, \text{N/C}) \cdot (2 \times 10^{-8} \, \text{C m}) \]

### Step 4: Perform the multiplication
\[ \tau = 5 \times 2 \times 10^{5} \times 10^{-8} \, \text{N m} \]
\[ \tau = 10 \times 10^{-3} \, \text{N m} = 10^{-2} \, \text{N m} \]

### Step 5: Conclusion
The maximum torque on the dipole is:
\[ \tau = 10^{-2} \, \text{N m} \]