An electric dipole consisting of two opposite charges of magnitude `3 xx 10^6` C each, separated by a distance of 0.02 m, is placed in an electric field of `2 xx 10^5`N/C. The maximum torque on the dipole will be:

Options

A. `12 xx 10^(-2) Nm`
B. `12 xx 10^(-3) Nm`
C. `12 xx 10^(-5) Nm`
D. `12 xx 10^(-7) Nm`

Explanation

To find the maximum torque on the electric dipole, we can follow these steps:

### Step 1: Understand the formula for torque on a dipole
The torque (\(\tau\)) on an electric dipole in an electric field is given by the equation:
\[ \tau = \mathbf{p} \times \mathbf{E} \]
where \(\mathbf{p}\) is the dipole moment and \(\mathbf{E}\) is the electric field. The magnitude of the torque can also be expressed as:
\[ \tau = pE \sin \theta \]
where \(\theta\) is the angle between the dipole moment and the electric field.

### Step 2: Determine the maximum torque condition
The maximum torque occurs when \(\sin \theta\) is maximum, which is equal to 1. This happens when \(\theta = 90^\circ\). Therefore, the maximum torque can be simplified to:
\[ \tau_{\text{max}} = pE \]

### Step 3: Calculate the dipole moment (\(p\))
The dipole moment (\(p\)) is calculated using the formula:
\[ p = q \cdot d \]
where \(q\) is the charge and \(d\) is the distance between the charges. Given:
- \(q = 3 \times 10^{-6} \, \text{C}\)
- \(d = 0.02 \, \text{m}\)

Now, substituting the values:
\[ p = (3 \times 10^{-6} \, \text{C}) \cdot (0.02 \, \text{m}) = 6 \times 10^{-8} \, \text{C m} \]

### Step 4: Calculate the maximum torque
Now, we can calculate the maximum torque using the electric field strength (\(E\)):
\[ E = 2 \times 10^{5} \, \text{N/C} \]
Substituting the values into the torque equation:
\[ \tau_{\text{max}} = pE = (6 \times 10^{-8} \, \text{C m}) \cdot (2 \times 10^{5} \, \text{N/C}) \]
Calculating this gives:
\[ \tau_{\text{max}} = 12 \times 10^{-3} \, \text{N m} = 0.012 \, \text{N m} \]

### Final Answer
The maximum torque on the dipole is:
\[ \tau_{\text{max}} = 0.012 \, \text{N m} \]

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