What is the formula for susceptibility in physics?
2 Answers
In physics, susceptibility (\(\chi\)) is a measure of how much a material becomes magnetized in response to an applied magnetic field. It quantifies the extent to which a material can be magnetized. There are different types of susceptibility depending on the context (e.g., magnetic susceptibility, electric susceptibility). Here's a breakdown of the formulas for each type:
### 1. Magnetic Susceptibility
Magnetic susceptibility (\(\chi_m\)) is defined as:
\[ \chi_m = \frac{M}{H} \]
where:
- \(M\) is the magnetization of the material (the magnetic moment per unit volume).
- \(H\) is the applied magnetic field strength.
**Magnetization \(M\)** is given by:
\[ M = \frac{B - \mu_0 H}{\mu_0} \]
where:
- \(B\) is the magnetic flux density (or magnetic induction).
- \(\mu_0\) is the permeability of free space.
**Combining these**, you get:
\[ \chi_m = \frac{B - \mu_0 H}{\mu_0 H} \]
or more commonly:
\[ \chi_m = \frac{B/\mu_0 - H}{H} \]
### 2. Electric Susceptibility
Electric susceptibility (\(\chi_e\)) is a measure of how a dielectric material becomes polarized in response to an applied electric field. It is defined as:
\[ \chi_e = \frac{P}{\epsilon_0 E} \]
where:
- \(P\) is the electric polarization (the electric dipole moment per unit volume).
- \(\epsilon_0\) is the permittivity of free space.
- \(E\) is the applied electric field strength.
**Electric Polarization \(P\)** can also be expressed in terms of the electric displacement field \(D\) and the electric field \(E\):
\[ P = \epsilon_0 \chi_e E \]
Thus, the susceptibility can also be expressed as:
\[ \chi_e = \frac{P}{\epsilon_0 E} \]
### 3. General Susceptibility (for Various Fields)
In a more general sense, susceptibility in physics can be defined for various fields. For example, in the context of other types of interactions, susceptibility might have different forms, but it typically reflects the response of a system to an external perturbation.
In summary:
- **Magnetic Susceptibility** (\(\chi_m\)) measures the extent of magnetization in response to a magnetic field.
- **Electric Susceptibility** (\(\chi_e\)) measures the extent of polarization in response to an electric field.
### 1. Magnetic Susceptibility
Magnetic susceptibility (\(\chi_m\)) is defined as:
\[ \chi_m = \frac{M}{H} \]
where:
- \(M\) is the magnetization of the material (the magnetic moment per unit volume).
- \(H\) is the applied magnetic field strength.
**Magnetization \(M\)** is given by:
\[ M = \frac{B - \mu_0 H}{\mu_0} \]
where:
- \(B\) is the magnetic flux density (or magnetic induction).
- \(\mu_0\) is the permeability of free space.
**Combining these**, you get:
\[ \chi_m = \frac{B - \mu_0 H}{\mu_0 H} \]
or more commonly:
\[ \chi_m = \frac{B/\mu_0 - H}{H} \]
### 2. Electric Susceptibility
Electric susceptibility (\(\chi_e\)) is a measure of how a dielectric material becomes polarized in response to an applied electric field. It is defined as:
\[ \chi_e = \frac{P}{\epsilon_0 E} \]
where:
- \(P\) is the electric polarization (the electric dipole moment per unit volume).
- \(\epsilon_0\) is the permittivity of free space.
- \(E\) is the applied electric field strength.
**Electric Polarization \(P\)** can also be expressed in terms of the electric displacement field \(D\) and the electric field \(E\):
\[ P = \epsilon_0 \chi_e E \]
Thus, the susceptibility can also be expressed as:
\[ \chi_e = \frac{P}{\epsilon_0 E} \]
### 3. General Susceptibility (for Various Fields)
In a more general sense, susceptibility in physics can be defined for various fields. For example, in the context of other types of interactions, susceptibility might have different forms, but it typically reflects the response of a system to an external perturbation.
In summary:
- **Magnetic Susceptibility** (\(\chi_m\)) measures the extent of magnetization in response to a magnetic field.
- **Electric Susceptibility** (\(\chi_e\)) measures the extent of polarization in response to an electric field.
In physics, susceptibility is a measure of how much a material responds to an external force, such as an electric or magnetic field. There are different types of susceptibility depending on the context, but the two most common ones are:
1. **Magnetic Susceptibility (χₘ):**
This measures how much a material becomes magnetized in response to an applied magnetic field. The formula for magnetic susceptibility is:
\[
\chi_m = \frac{M}{H}
\]
where:
- \( \chi_m \) is the magnetic susceptibility,
- \( M \) is the magnetization of the material (the magnetic moment per unit volume),
- \( H \) is the magnetic field strength.
Magnetic susceptibility can be related to the permeability of the material through the formula:
\[
\chi_m = \frac{\mu_r - 1}{\mu_0}
\]
where:
- \( \mu_r \) is the relative permeability of the material,
- \( \mu_0 \) is the permeability of free space.
2. **Electric Susceptibility (χₑ):**
This measures how much a material becomes polarized in response to an applied electric field. The formula for electric susceptibility is:
\[
\chi_e = \frac{P}{\epsilon_0 E}
\]
where:
- \( \chi_e \) is the electric susceptibility,
- \( P \) is the electric polarization of the material (the electric dipole moment per unit volume),
- \( \epsilon_0 \) is the permittivity of free space,
- \( E \) is the electric field strength.
Electric susceptibility is related to the relative permittivity (\( \epsilon_r \)) of the material by:
\[
\chi_e = \epsilon_r - 1
\]
where:
- \( \epsilon_r \) is the relative permittivity (also known as the dielectric constant) of the material.
In both cases, susceptibility provides insight into how a material interacts with external fields and helps in understanding its electrical or magnetic properties.
1. **Magnetic Susceptibility (χₘ):**
This measures how much a material becomes magnetized in response to an applied magnetic field. The formula for magnetic susceptibility is:
\[
\chi_m = \frac{M}{H}
\]
where:
- \( \chi_m \) is the magnetic susceptibility,
- \( M \) is the magnetization of the material (the magnetic moment per unit volume),
- \( H \) is the magnetic field strength.
Magnetic susceptibility can be related to the permeability of the material through the formula:
\[
\chi_m = \frac{\mu_r - 1}{\mu_0}
\]
where:
- \( \mu_r \) is the relative permeability of the material,
- \( \mu_0 \) is the permeability of free space.
2. **Electric Susceptibility (χₑ):**
This measures how much a material becomes polarized in response to an applied electric field. The formula for electric susceptibility is:
\[
\chi_e = \frac{P}{\epsilon_0 E}
\]
where:
- \( \chi_e \) is the electric susceptibility,
- \( P \) is the electric polarization of the material (the electric dipole moment per unit volume),
- \( \epsilon_0 \) is the permittivity of free space,
- \( E \) is the electric field strength.
Electric susceptibility is related to the relative permittivity (\( \epsilon_r \)) of the material by:
\[
\chi_e = \epsilon_r - 1
\]
where:
- \( \epsilon_r \) is the relative permittivity (also known as the dielectric constant) of the material.
In both cases, susceptibility provides insight into how a material interacts with external fields and helps in understanding its electrical or magnetic properties.