Is electric field intensity scalar or vector?
2 Answers
Electric field intensity, also known as electric field, is a vector quantity. This means it has both magnitude and direction.
To elaborate:
- **Magnitude**: This is how strong the electric field is at a particular point. It tells you the force experienced by a positive test charge placed in the field.
- **Direction**: This indicates the direction in which a positive test charge would be pushed or pulled by the field.
Mathematically, the electric field intensity \( \mathbf{E} \) at a point in space is defined as:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where \( \mathbf{F} \) is the force experienced by a positive test charge \( q \).
In vector form, the electric field due to a point charge \( Q \) located at a position \( \mathbf{r}_0 \) is given by:
\[ \mathbf{E}(\mathbf{r}) = \frac{1}{4 \pi \epsilon_0} \frac{Q}{|\mathbf{r} - \mathbf{r}_0|^2} \hat{\mathbf{r}} \]
where:
- \( \mathbf{r} \) is the position vector of the point where the field is being calculated,
- \( \mathbf{r}_0 \) is the position vector of the charge,
- \( \hat{\mathbf{r}} \) is the unit vector in the direction from \( Q \) to the point where the field is being measured,
- \( \epsilon_0 \) is the permittivity of free space.
This vector nature of the electric field is crucial for understanding and analyzing various electrical phenomena, such as how charges interact with each other and how electric fields influence the movement of charges.
To elaborate:
- **Magnitude**: This is how strong the electric field is at a particular point. It tells you the force experienced by a positive test charge placed in the field.
- **Direction**: This indicates the direction in which a positive test charge would be pushed or pulled by the field.
Mathematically, the electric field intensity \( \mathbf{E} \) at a point in space is defined as:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where \( \mathbf{F} \) is the force experienced by a positive test charge \( q \).
In vector form, the electric field due to a point charge \( Q \) located at a position \( \mathbf{r}_0 \) is given by:
\[ \mathbf{E}(\mathbf{r}) = \frac{1}{4 \pi \epsilon_0} \frac{Q}{|\mathbf{r} - \mathbf{r}_0|^2} \hat{\mathbf{r}} \]
where:
- \( \mathbf{r} \) is the position vector of the point where the field is being calculated,
- \( \mathbf{r}_0 \) is the position vector of the charge,
- \( \hat{\mathbf{r}} \) is the unit vector in the direction from \( Q \) to the point where the field is being measured,
- \( \epsilon_0 \) is the permittivity of free space.
This vector nature of the electric field is crucial for understanding and analyzing various electrical phenomena, such as how charges interact with each other and how electric fields influence the movement of charges.