Steady current conditions and conduction laws

1. Current intensity and current density

There are a large number of charged particles that can move freely in the conductor. The directional movement of charged particles forms an electric current. The charged particles that provide the current are called carriers. In metal conductors, the carriers are free electrons, in electrolyte conductors, the carriers are positive and negative ions, and in ionized gases, the carriers are positive and negative ions and electrons. In this chapter, we mainly discuss the case of metal conductors.

In general conductors, when there is no electric field, the carriers only move in a thermal manner and do not form a current. When an electric field is applied, the carriers will move in a directional manner to form a current. However, this electric field should not be an electrostatic field, because when an electrostatic field acts on a conductor, an electrostatic equilibrium will occur, the electric field inside the conductor will disappear, and the current can only last for a short moment. How to apply an electric field to the inside of a conductor will be discussed at the end of this section.

In order to describe the strength of the current, we introduce the quantity of current intensity, which is defined as the amount of electricity passing through a conductor cross section per unit time, and is usually represented by the symbol I. Current intensity is often referred to as current. If the amount of electricity passing through a certain cross section of a conductor in a time period of d t is d Q , then the current passing through the cross section is

. (10-1)

The current intensity is a scalar quantity, but since the charge flows in the wire in two directions, positive and negative, the current can be positive or negative, and is an algebraic quantity. The positive and negative of the current is determined according to the pre-selected calibration direction. The current flowing in the same direction as the calibration direction is positive current, and the current flowing in the opposite direction to the calibration direction is negative current.

We usually take the flow direction of positive carriers to represent the direction of current. Obviously, the current formed by the flow of positive carriers in a certain direction is equivalent to the current formed by the flow of negative carriers in the opposite direction. This equivalence is limited to the magnitude and direction of the current formed by the carriers, the magnetic field generated by the current, etc., while for the Hall effect, the chemical effect of current, etc., the movement of positive carriers and the movement of negative carriers in the opposite direction have different effects.

In the International System of Units, current intensity is one of the seven basic physical quantities, and its unit A (ampere) is one of the seven basic units. We will give the definition of this unit later.

The current intensity reflects the condition of carriers passing through the entire cross-section of the conductor per unit time, and does not involve the details of the carriers passing through each part of the cross-section. If the thickness of the conductor is uneven, the distribution of carriers at each part of the large cross-section and each part of the small cross-section is obviously different. In order to describe the distribution of current, it is necessary to introduce another physical quantity, namely current density. The current density is a vector. Its direction at any point in the conductor is the same as the flow direction of positive carriers at that point, and its magnitude is equal to the current intensity per unit cross-section passing through the point and perpendicular to the current. If the current intensity of the surface element d S perpendicular to the current direction at a point in the conductor is d I , then the current density at that point can be expressed as

, (10-2) where n is the normal unit vector of the surface element d S. If the other surface element d S ¢ at the same point is not perpendicular to the current, there is an angle q between its normal n ¢ and the current density j at that point , as shown in Figure 10-1. According to formula (10-2), the magnitude of the current density at that point can be expressed as

,

so

. (10-3)

The above formula indicates that the current intensity per unit area of ​​any surface element is equal to the component of the current density vector at that location along the normal direction of the surface element.

In the International System of Units, the unit of current density is A × m ^{- 2} (ampere/meter ² ).

From the definition of current density, we know that the current I passing through any surface S in the conductor can be expressed as

. (10-4)

Comparing the above formula with the electric flux definition formula (9-22), it can be seen that the relationship between I and j is the relationship between a flux and its vector field. In a conductor with current flowing through it, each point has a current density vector of a certain magnitude and direction. These vectors constitute a vector field, called a current field. In order to vividly describe the distribution of current in the current field, current lines are introduced. Current lines are a series of curves drawn according to the following regulations: the tangent direction of each point on the curve is the same as the direction of the current density vector at that point. The tubular area surrounded by current lines is called a current tube. Obviously, under constant conditions, the current passing through any cross section of the same current tube is equal.