Magnetic Field Due to a Long Straight Current-Carrying Conductor

by
When an electric current flows through a conductor, it produces a magnetic field around it. This fundamental idea, confirmed by Oersted’s experiment, forms the foundation of electromagnetism.
Magnetic Field Due to a Long Straight Current-Carrying Conductor.-conductor
conductor
One of the simplest systems for studying this phenomenon is a long straight current-carrying wire. Understanding the magnetic field around such a conductor is vital for analysing electric circuits, power transmission lines, and many electromagnetic devices.

Magnetic Field Due to a Long Straight Current-Carrying Conductor

Introduction

A long straight conductor carrying a steady current generates circular magnetic field lines around it. These field lines form concentric circles centered on the wire. The direction of the magnetic field depends on the direction of the current and is determined using the Right-Hand Thumb Rule.
This situation is idealised because we consider the wire “long,” meaning its length is much greater than the distance from the observation point. This assumption ensures that the field is symmetrical and can be easily described mathematically.

Right-Hand Thumb Rule

To determine the direction of the magnetic field around a straight conductor:
Hold the conductor in your right hand.
Place the thumb in the direction of the current.
Then the curled fingers around the conductor show the direction of magnetic field lines.
If the current flows upward, the magnetic field circulates anticlockwise around the wire. If it flows downward, the field circulates clockwise.
This rule helps visualise the orientation of magnetic lines of force around the wire.

Derivation Using Biot–Savart Law

The magnitude of the magnetic field at a distance ‘r’ from a long straight conductor carrying current ‘I’ can be derived using the Biot–Savart Law, which states: dB = µ0 / 4π . I dl sinΦ / r2
For a long straight wire, every small segment of the wire contributes to the magnetic field at the observation point.
By integrating over the entire infinite length of the wire, we get:
B = µ0I / 2πr
Here,
( B ) = magnetic field
(µ0) = permeability of free space (4π x 10-7) T·m/A )
( I ) = current in the wire
( r ) = perpendicular distance from the conductor

Key Observations:

The magnetic field is directly proportional to the current: More current produces a stronger field.
The magnetic field is inversely proportional to the distance: The farther we move from the wire, the weaker the magnetic field becomes.
The field is always perpendicular to the radius vector and tangent to the circular field lines.

Magnetic Field Pattern

The magnetic field lines around a straight current-carrying conductor:
Are circular and concentric.
Do not intersect each other.
Become denser near the wire (indicating stronger field).
Spread out as distance increases.
The pattern demonstrates that the magnetic field is strongest near the conductor and gradually weakens as we move away.

Dependence on Direction of Current

The direction of magnetic field changes when the direction of current changes. This phenomenon is vital in devices like:
Electromagnets
Solenoids
Electric motors
Induction coils
By controlling the direction of current, we can manipulate the magnetic field produced.
Solenoids
electric motors

Applications

Transmission Lines
Long straight conductors are used in power transmission. Studying the magnetic field helps understand the forces between parallel conductors. Two parallel current-carrying wires exert forces on each other attraction if currents are in the same direction, repulsion if opposite.

Electromagnets and Motors

The basic principle of magnetic field generation in motors stems from current-carrying conductors. Understanding the field around a straight wire helps explain torque generation in motor coils.

Measurement Devices

In galvanometers and ammeters, magnetic fields interact with moving coils or conductors, and the underlying concept originates from the field due to straight conductors.

Magnetic Field Sensors

Hall effect sensors measure the magnetic field caused by current in conductors, used widely in automotive and electronic devices.

Force Between Two Parallel Conductors

Two long straight conductors carrying currents I1 and I2 separated by distance ( r ) produce magnetic fields that influence each other.
The force per unit length is:
F = µ0 I1 I2 / 2πr
This principle defines the ampere, the SI unit of current.

Summary

A long straight conductor carrying current produces a magnetic field of magnitude
  B =  µ0I / 2πr
The field lines are circular and centered on the wire.

Direction of field is given by the Right-Hand Thumb Rule.

Magnetic field decreases as distance increases.
Principles based on straight conductors enable the functioning of motors, transformers, sensors, and power lines.
A magnetic field is produced around any conductor through which electric current flows. For a long straight conductor, this magnetic field forms concentric circular lines around the wire.
 
The Right-Hand Thumb Rule is used. If you hold the conductor in your right hand with the thumb pointing in the direction of current, your curled fingers show the direction of the magnetic field lines.
 
B = µ0I / 2πr
Here,
( B ) = magnetic field
(µ0) = permeability of free space (4π x 10-7) T·m/A )
( I ) = current in the wire
( r ) = perpendicular distance from the conductor
The magnetic field is inversely proportional to the distance.
As the distance increases, the magnetic field becomes weaker.
 
The magnetic field is directly proportional to the current. When current increases, the strength of the magnetic field also increases.
 
The magnetic field lines form concentric circles centered on the conductor.
 
There are two methods:
Increase the current flowing through the wire.
Decrease the distance from the conductor (move closer to the wire).

Leave a comment