What is the relation between electric field intensity and force?
2 Answers
The relationship between **electric field intensity** (also known as **electric field strength**) and **force** is fundamental to understanding how charged particles interact with electric fields. This relationship can be explained using **Coulomb's Law** and the definition of the **electric field**.
### 1. **Definition of Electric Field Intensity**:
Electric field intensity (\( \mathbf{E} \)) at a point in space is defined as the force (\( \mathbf{F} \)) experienced by a small positive test charge (\( q \)) placed at that point, divided by the magnitude of the charge. It tells us how much force per unit charge a test charge would experience at a particular location due to the presence of electric charges.
Mathematically, the electric field intensity is given by the equation:
\[
\mathbf{E} = \frac{\mathbf{F}}{q}
\]
Where:
- \( \mathbf{E} \) is the electric field intensity (measured in volts per meter or \( \text{N/C} \), newtons per coulomb),
- \( \mathbf{F} \) is the force exerted on the test charge (measured in newtons),
- \( q \) is the magnitude of the test charge (measured in coulombs).
### 2. **Relation between Electric Field and Force**:
From the definition of electric field intensity, the force \( \mathbf{F} \) on a charge \( q \) in an electric field \( \mathbf{E} \) can be expressed as:
\[
\mathbf{F} = q \mathbf{E}
\]
This equation shows that the force experienced by a charge in an electric field is directly proportional to both the magnitude of the electric field and the charge itself.
- **\( \mathbf{F} \)** is the force acting on the charge,
- **\( q \)** is the charge,
- **\( \mathbf{E} \)** is the electric field intensity.
The direction of the force depends on the sign of the charge:
- If the charge is **positive**, the force is in the **same direction** as the electric field.
- If the charge is **negative**, the force is in the **opposite direction** to the electric field.
### 3. **Coulomb’s Law and Electric Field**:
Coulomb's Law describes the force between two point charges. If there are two charges, \( q_1 \) and \( q_2 \), separated by a distance \( r \), the force between them is given by:
\[
\mathbf{F} = k_e \frac{q_1 q_2}{r^2} \hat{r}
\]
Where:
- \( k_e \) is Coulomb’s constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)),
- \( r \) is the distance between the charges,
- \( \hat{r} \) is the unit vector along the line joining the two charges.
Now, the electric field produced by a point charge \( q \) at a distance \( r \) from the charge can be found by substituting Coulomb's Law into the definition of the electric field:
\[
\mathbf{E} = k_e \frac{q}{r^2} \hat{r}
\]
This shows that the electric field decreases with the square of the distance from the charge and is directly proportional to the charge producing the field.
### 4. **Key Takeaways**:
- The **electric field intensity** is a measure of the force per unit charge at a given point in space.
- The **force** experienced by a charge in an electric field is given by \( \mathbf{F} = q \mathbf{E} \).
- **Positive charges** experience a force in the direction of the electric field, while **negative charges** experience a force in the opposite direction.
- The electric field produced by a point charge decreases with distance, according to an inverse square law.
In summary, the **electric field intensity** describes how strong and in which direction the electric field is at a point, while the **force** on a charge in that field is directly proportional to both the electric field and the charge itself.
### 1. **Definition of Electric Field Intensity**:
Electric field intensity (\( \mathbf{E} \)) at a point in space is defined as the force (\( \mathbf{F} \)) experienced by a small positive test charge (\( q \)) placed at that point, divided by the magnitude of the charge. It tells us how much force per unit charge a test charge would experience at a particular location due to the presence of electric charges.
Mathematically, the electric field intensity is given by the equation:
\[
\mathbf{E} = \frac{\mathbf{F}}{q}
\]
Where:
- \( \mathbf{E} \) is the electric field intensity (measured in volts per meter or \( \text{N/C} \), newtons per coulomb),
- \( \mathbf{F} \) is the force exerted on the test charge (measured in newtons),
- \( q \) is the magnitude of the test charge (measured in coulombs).
### 2. **Relation between Electric Field and Force**:
From the definition of electric field intensity, the force \( \mathbf{F} \) on a charge \( q \) in an electric field \( \mathbf{E} \) can be expressed as:
\[
\mathbf{F} = q \mathbf{E}
\]
This equation shows that the force experienced by a charge in an electric field is directly proportional to both the magnitude of the electric field and the charge itself.
- **\( \mathbf{F} \)** is the force acting on the charge,
- **\( q \)** is the charge,
- **\( \mathbf{E} \)** is the electric field intensity.
The direction of the force depends on the sign of the charge:
- If the charge is **positive**, the force is in the **same direction** as the electric field.
- If the charge is **negative**, the force is in the **opposite direction** to the electric field.
### 3. **Coulomb’s Law and Electric Field**:
Coulomb's Law describes the force between two point charges. If there are two charges, \( q_1 \) and \( q_2 \), separated by a distance \( r \), the force between them is given by:
\[
\mathbf{F} = k_e \frac{q_1 q_2}{r^2} \hat{r}
\]
Where:
- \( k_e \) is Coulomb’s constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)),
- \( r \) is the distance between the charges,
- \( \hat{r} \) is the unit vector along the line joining the two charges.
Now, the electric field produced by a point charge \( q \) at a distance \( r \) from the charge can be found by substituting Coulomb's Law into the definition of the electric field:
\[
\mathbf{E} = k_e \frac{q}{r^2} \hat{r}
\]
This shows that the electric field decreases with the square of the distance from the charge and is directly proportional to the charge producing the field.
### 4. **Key Takeaways**:
- The **electric field intensity** is a measure of the force per unit charge at a given point in space.
- The **force** experienced by a charge in an electric field is given by \( \mathbf{F} = q \mathbf{E} \).
- **Positive charges** experience a force in the direction of the electric field, while **negative charges** experience a force in the opposite direction.
- The electric field produced by a point charge decreases with distance, according to an inverse square law.
In summary, the **electric field intensity** describes how strong and in which direction the electric field is at a point, while the **force** on a charge in that field is directly proportional to both the electric field and the charge itself.
The relationship between electric field intensity (\( \mathbf{E} \)) and force (\( \mathbf{F} \)) is fundamental to understanding how electric fields interact with charges. Here’s a detailed explanation:
### 1. **Electric Field Intensity (\( \mathbf{E} \))**
The electric field intensity at a point in space is defined as the force experienced by a positive test charge placed at that point per unit charge. Mathematically, it is given by:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where:
- \( \mathbf{E} \) is the electric field intensity,
- \( \mathbf{F} \) is the force experienced by the test charge,
- \( q \) is the magnitude of the test charge.
### 2. **Force (\( \mathbf{F} \))**
The force experienced by a charge \( q \) in an electric field \( \mathbf{E} \) is given by:
\[ \mathbf{F} = q \mathbf{E} \]
where:
- \( \mathbf{F} \) is the force experienced by the charge,
- \( q \) is the charge,
- \( \mathbf{E} \) is the electric field intensity at the location of the charge.
### **Relation Between Electric Field Intensity and Force**
From the above equations, you can see that:
- The electric field intensity \( \mathbf{E} \) determines how strong the electric field is at a point in space.
- The force \( \mathbf{F} \) experienced by a charge \( q \) is directly proportional to both the electric field intensity \( \mathbf{E} \) and the magnitude of the charge \( q \).
In essence, the electric field intensity is a measure of the electric force per unit charge. The force experienced by a charge in an electric field is the product of the charge and the electric field intensity.
### **Example**
If you have an electric field \( \mathbf{E} \) of 100 N/C (newtons per coulomb) and you place a charge of 2 C (coulombs) in this field, the force \( \mathbf{F} \) on the charge is:
\[ \mathbf{F} = q \mathbf{E} = 2 \, \text{C} \times 100 \, \text{N/C} = 200 \, \text{N} \]
Thus, the charge experiences a force of 200 newtons in the direction of the electric field.
### **Summary**
- The electric field intensity \( \mathbf{E} \) is defined as the force per unit charge.
- The force \( \mathbf{F} \) on a charge \( q \) in an electric field \( \mathbf{E} \) is the product of the charge and the electric field intensity.
Understanding this relationship is crucial in many areas of electromagnetism and electrical engineering, as it underpins how charges interact within electric fields.
### 1. **Electric Field Intensity (\( \mathbf{E} \))**
The electric field intensity at a point in space is defined as the force experienced by a positive test charge placed at that point per unit charge. Mathematically, it is given by:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where:
- \( \mathbf{E} \) is the electric field intensity,
- \( \mathbf{F} \) is the force experienced by the test charge,
- \( q \) is the magnitude of the test charge.
### 2. **Force (\( \mathbf{F} \))**
The force experienced by a charge \( q \) in an electric field \( \mathbf{E} \) is given by:
\[ \mathbf{F} = q \mathbf{E} \]
where:
- \( \mathbf{F} \) is the force experienced by the charge,
- \( q \) is the charge,
- \( \mathbf{E} \) is the electric field intensity at the location of the charge.
### **Relation Between Electric Field Intensity and Force**
From the above equations, you can see that:
- The electric field intensity \( \mathbf{E} \) determines how strong the electric field is at a point in space.
- The force \( \mathbf{F} \) experienced by a charge \( q \) is directly proportional to both the electric field intensity \( \mathbf{E} \) and the magnitude of the charge \( q \).
In essence, the electric field intensity is a measure of the electric force per unit charge. The force experienced by a charge in an electric field is the product of the charge and the electric field intensity.
### **Example**
If you have an electric field \( \mathbf{E} \) of 100 N/C (newtons per coulomb) and you place a charge of 2 C (coulombs) in this field, the force \( \mathbf{F} \) on the charge is:
\[ \mathbf{F} = q \mathbf{E} = 2 \, \text{C} \times 100 \, \text{N/C} = 200 \, \text{N} \]
Thus, the charge experiences a force of 200 newtons in the direction of the electric field.
### **Summary**
- The electric field intensity \( \mathbf{E} \) is defined as the force per unit charge.
- The force \( \mathbf{F} \) on a charge \( q \) in an electric field \( \mathbf{E} \) is the product of the charge and the electric field intensity.
Understanding this relationship is crucial in many areas of electromagnetism and electrical engineering, as it underpins how charges interact within electric fields.