A sample of HCl gas is placed in an electrical field of `3 xx 10^(4)NC^(-1)`. The dipole moment of each HCl molecule is `6 xx 10^(-30) C -m`. The maximum torque that can act on a molecule is

Options

A. `2 xx 10^(-34) C^(2)N^(-1)m`
B. `2 xx 10^(-34) N - m`
C. `18 xx 10^(-26) N - m`
D. `0.5 xx 10^(34) C^(-2) N^(-1) m^(-1)`

Answer

To find the maximum torque acting on an HCl molecule placed in an electric field, we can follow these steps:

### Step 1: Understand the formula for torque on a dipole in an electric field
The torque (τ) experienced by a dipole in an electric field is given by the formula:
\[ \tau = \mathbf{p} \times \mathbf{E} \]
Where:
- \( \tau \) is the torque,
- \( \mathbf{p} \) is the dipole moment,
- \( \mathbf{E} \) is the electric field.

### Step 2: Determine the magnitude of the torque
The magnitude of the torque can be expressed as:
\[ |\tau| = pE \sin \theta \]
Where:
- \( p \) is the dipole moment,
- \( E \) is the magnitude of the electric field,
- \( \theta \) is the angle between the dipole moment and the electric field.

### Step 3: Identify the maximum torque condition
The maximum torque occurs when \( \sin \theta = 1 \), which corresponds to \( \theta = 90^\circ \). Therefore, the maximum torque can be expressed as:
\[ \tau_{\text{max}} = pE \]

### Step 4: Substitute the given values
Given:
- Dipole moment \( p = 6 \times 10^{-30} \, \text{C m} \)
- Electric field \( E = 3 \times 10^{4} \, \text{N/C} \)

Substituting these values into the equation for maximum torque:
\[ \tau_{\text{max}} = (6 \times 10^{-30} \, \text{C m}) \times (3 \times 10^{4} \, \text{N/C}) \]

### Step 5: Calculate the maximum torque
Now, performing the multiplication:
\[ \tau_{\text{max}} = 18 \times 10^{-26} \, \text{N m} \]

### Final Result
Thus, the maximum torque that can act on an HCl molecule in the given electric field is:
\[ \tau_{\text{max}} = 1.8 \times 10^{-25} \, \text{N m} \]

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