19.5 Electrical Conductivity
19.5.1 Relation between J and E
- Whenever current flows in a conducting material, we will have a current density J at any point in the material. At the same time, there has to be an electric field of magnitude E existing at any point within that material so that charges are forced to move through the material. Hence, vector J and vector E are found at the same point.
Figure 19.7 Flow of electrical charges under an applied electric field. When an electric field (E) is applied to a conductor, positive charges move in the direction of the field, while negative charges move in the opposite direction. This motion of charges produces an electric current, and the distribution of this current is described by the current density (J), where J = σE. - The magnitude of J is a measure of the amount of charge flowing per unit time through a very small area. The rate of charge flow has to be determined by the electric force acting on the charges. The electric force is in turn determined by the electric field strength E. This implies that J has to be related to E.
- At constant temperature, the two vectors are related to each other through the relationship:
$J\propto E$or$\boxed{J=\sigma E}$
where σ is a constant (at constant temperature) known as the electrical conductivity of the material. J points in the direction of E, and E points in the direction of positive charge flow.
19.5.2 Electrical Conductivity
1. Meaning
Electrical conductivity σ is a physical quantity whose magnitude reflects the ability of a material to conduct electric current. A material like copper, which conducts electricity much better than a material like silicon, has a much higher value of electrical conductivity.
2. Unit
The unit of σ is siemens per metre (S m-1) or Ω-1 m-1.
3. Some values of σ
The values of σ of some materials are shown in the table at the side.
Example 19.7
A constant current of 5.0 A flows in a uniform copper wire of diameter 1.0 mm. Determine the p.d. applied across 10 cm of the wire.
(For copper, σ = 5.7 × 107 S m-1)
Answer
Cross-sectional area:
A = 1/4 πd² = 1/4 π(1.0 × 10-3)² = 7.85 × 10-7 m²
Current density:
J = I / A = 5.0 / (7.85 × 10-7) = 6.37 × 106 A m-2
Electric field strength:
E = J / σ = (6.37 × 106) / (5.7 × 107) = 0.11 V m-1
But,
E = V / L
V = EL = (0.11)(0.10) = 0.011 V
19.5.3 Equation for σ
Suppose a p.d. is applied across a conductor so that an electric field is produced within the conductor. A conduction electron will accelerate within the conductor since it is acted upon by an electric force.
F = ma
where F and m represent the electric force acting on the electron and the mass of the electron respectively. But F is given by:
F = eE
Hence,
ma = eE
a = eE / m
Let the mean time interval, known as the mean free time, between collisions made by conduction electrons be t. Assume that the speed of the conduction electron drops to zero after colliding with an atom and then increases uniformly to v after time t.
v = at
The average speed (drift velocity) is:
vd = (0 + v)/2 = 1/2 at = 1/2 (eE/m)t
But,
vd = J / ne
Hence,
J / ne = 1/2 (eE/m)t
J = (ne²t / 2m) E
For a material which obeys:
J = σE
we get:
σ = ne²t / 2m
Applications of Electrical Conductivity in Daily Life and Industry
Electrical conductivity is a property of materials that allows them to conduct electric current. Understanding and utilizing this property is essential in electronics, industrial processes, and everyday life.
1. Electrical Wiring
Materials with high electrical conductivity, such as copper and aluminum, are commonly used in electrical wiring.
2. Electronics and Circuits
In electronic devices, components like capacitors, resistors, and diodes rely on conductivity properties.
3. Sensors and Measurement Devices
Sensors such as temperature sensors and strain gauges operate based on conductivity changes.
4. Industrial Applications
Electrical conductivity is essential in electroplating, battery manufacturing, and chemical processing.
5. Everyday Products
Applications include touchscreens, heating elements, and electric kettles.
Conclusion: Electrical Conductivity
Electrical conductivity is a fundamental property of materials that determines how easily electric current can flow through them. It depends on the presence and mobility of charge carriers such as electrons.
The relationship between current density and electric field, expressed as J = σE, shows that conductivity plays a key role in controlling the efficiency of current flow. Materials with high conductivity, such as metals, allow charges to move freely, while insulating materials resist the flow of electricity.
Understanding electrical conductivity is essential in physics and engineering, as it is widely applied in electrical systems, electronic devices, and modern technology. It also helps explain important effects such as resistance, heating, and energy transfer.
Frequently Asked Questions (FAQ) – Electrical Conductivity
What is electrical conductivity?
Electrical conductivity is the ability of a material to conduct electric current. It depends on the number and mobility of charge carriers such as electrons.
What is the SI unit of electrical conductivity?
The SI unit of electrical conductivity is siemens per meter (S/m), also written as Ω⁻¹ m⁻¹.
What is the formula for electrical conductivity?
The relationship between current density and electric field is given by J = σE, where σ is the electrical conductivity.
What factors affect electrical conductivity?
Electrical conductivity is affected by temperature, material type, number of charge carriers, and impurities.
Why are metals good conductors?
Metals are good conductors because they contain many free electrons that can move easily under an electric field.
Keywords: electrical conductivity, applications, current density
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