Is electric field dependent on area of cross section?
2 Answers
The electric field itself is not directly dependent on the area of the cross-section of a conductor or any other object. Instead, the electric field is determined by the charge distribution and the distance from the source of the electric field.
To clarify, here are some key points about the electric field:
1. **Definition of Electric Field**: The electric field (\( \mathbf{E} \)) at a point in space is defined as the force per unit charge experienced by a positive test charge placed at that point. Mathematically, it is given by:
\[
\mathbf{E} = \frac{\mathbf{F}}{q}
\]
where \( \mathbf{F} \) is the force and \( q \) is the charge.
2. **Electric Field of a Point Charge**: For a point charge, the electric field at a distance \( r \) from the charge is given by Coulomb's law:
\[
E = \frac{k \cdot Q}{r^2}
\]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the distance from the charge. This expression shows that the electric field depends on the charge and the distance but not on the area of any cross-sectional area.
3. **Electric Field in a Conductor**: In the case of a conductor, if we apply a voltage across it, the electric field inside the conductor is related to the voltage \( V \) and the length \( L \) of the conductor by:
\[
E = \frac{V}{L}
\]
Here, the electric field is dependent on the voltage and the length of the conductor but not on its cross-sectional area.
4. **Electric Field and Charge Distribution**: If we consider a conductor with a given charge distribution, the electric field depends on the total charge and its distribution relative to the point where the field is measured. The area of the cross-section of the conductor affects the amount of current that can flow through the conductor for a given voltage (by Ohm's law), but not the electric field itself.
In summary, while the cross-sectional area of a conductor affects the resistance and current flow, it does not affect the electric field directly. The electric field is a function of charge distribution and distance from the source.
To clarify, here are some key points about the electric field:
1. **Definition of Electric Field**: The electric field (\( \mathbf{E} \)) at a point in space is defined as the force per unit charge experienced by a positive test charge placed at that point. Mathematically, it is given by:
\[
\mathbf{E} = \frac{\mathbf{F}}{q}
\]
where \( \mathbf{F} \) is the force and \( q \) is the charge.
2. **Electric Field of a Point Charge**: For a point charge, the electric field at a distance \( r \) from the charge is given by Coulomb's law:
\[
E = \frac{k \cdot Q}{r^2}
\]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the distance from the charge. This expression shows that the electric field depends on the charge and the distance but not on the area of any cross-sectional area.
3. **Electric Field in a Conductor**: In the case of a conductor, if we apply a voltage across it, the electric field inside the conductor is related to the voltage \( V \) and the length \( L \) of the conductor by:
\[
E = \frac{V}{L}
\]
Here, the electric field is dependent on the voltage and the length of the conductor but not on its cross-sectional area.
4. **Electric Field and Charge Distribution**: If we consider a conductor with a given charge distribution, the electric field depends on the total charge and its distribution relative to the point where the field is measured. The area of the cross-section of the conductor affects the amount of current that can flow through the conductor for a given voltage (by Ohm's law), but not the electric field itself.
In summary, while the cross-sectional area of a conductor affects the resistance and current flow, it does not affect the electric field directly. The electric field is a function of charge distribution and distance from the source.