A current exists in a wire that gradually narrows down to a smaller diameter. How do the drift velocity, the current density, and the electric field vary along the wire?
Can you please help explain this?
As the wire shrinks in diameter, its resistance increases, and total current decreases. Drift velocity, E-field and current density (per area of wire cross section) remain the same.
Certainly! In a wire carrying electric current, there are three important factors to consider: drift velocity, current density, and electric field.
1. Drift velocity: The drift velocity refers to the average velocity at which the electrons move through the wire. In a wire with a constant cross-sectional area, the drift velocity remains constant along the length of the wire. However, if the wire narrows down to a smaller diameter, the drift velocity increases. This is because if the same amount of current needs to flow through a smaller area, the electrons must move faster to maintain a steady flow of charge.
2. Current density: Current density is defined as the amount of current flowing through a unit area perpendicular to the direction of current flow. Mathematically, it is given by the equation J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the wire. If the wire gradually narrows down, the cross-sectional area decreases. As a result, the current density increases because the same amount of current is flowing through a smaller area. So, the current density increases along the wire as it narrows.
3. Electric field: The electric field is a measure of the force exerted on a charge per unit charge. In a wire, the electric field drives the movement of electrons. As the wire narrows down, the electric field does not change significantly along the wire, assuming there are no external factors influencing it. The electric field is determined by the voltage or potential difference applied across the wire and the length of the wire. The electric field remains constant along the wire unless there are other factors such as resistors or changes in the wire's material affecting it.
In summary, as the wire narrows down, the drift velocity of electrons increases, the current density increases, but the electric field remains relatively constant along the wire.