Which of the following is true about linear isotropic dielectric ?

Options

A. Induced dipole moment of the linear isotropic dielectric is opposite to the direction of external electric field and proportional to the field strength
B. Induced dipole moment of the linear isotropic dielectric is in the direction of the field and proportional to the field strength
C. Induced dipole moment of the linear isotropic dielectric is perpendicular to the direction of external field and proportional to the field strength
D. Induced dipole moment of the linear isotropic dielectric is independent to the direction of external field and the field strength

Answer

To determine the true statement about linear isotropic dielectrics, let's analyze the characteristics of induced dipole moments in such materials step by step.

### Step 1: Understanding Dielectrics
A dielectric is a non-conducting material that can be polarized by an external electric field. When an electric field is applied, the charges within the dielectric material shift slightly, creating induced dipole moments.

**Hint:** Remember that dielectrics do not conduct electricity but can respond to electric fields.

### Step 2: Direction of Induced Dipole Moment
In a linear isotropic dielectric, when an external electric field is applied, the induced dipole moment aligns with the direction of the electric field. The negative charges in the dielectric are attracted towards the positive side of the electric field, while positive charges are repelled towards the negative side, leading to a net dipole moment in the direction of the electric field.

**Hint:** Visualize how charges move in response to an electric field to understand the direction of the dipole moment.

### Step 3: Proportionality to Electric Field Strength
The induced dipole moment (p) in a dielectric is proportional to the strength of the applied electric field (E). This means that as the strength of the electric field increases, the separation of the induced charges also increases, leading to a larger dipole moment. Mathematically, this can be expressed as:
\[ p \propto E \]

**Hint:** Think about how stronger electric fields cause more significant charge separation within the dielectric.

### Step 4: Conclusion
Based on the above analysis, we can conclude that:
- The induced dipole moment in a linear isotropic dielectric is in the same direction as the applied electric field.
- The induced dipole moment is proportional to the strength of the electric field.

Thus, the correct statement about linear isotropic dielectrics is that the induced dipole moment is in the direction of the electric field and is proportional to the field strength.

**Final Answer:** The induced dipole moment of a linear isotropic dielectric is in the direction of the electric field and proportional to the electric field strength.