Magnetic Field Due to Electric Current - Detailed Theory & Diagrams

🧲 Magnetic Field Due to Electric Current

📚 What is a Magnetic Field?

A magnetic field is a vector field around a magnet, electric current, or changing electric field where magnetic forces are exerted on moving charges and magnetic materials. It is invisible but can be visualized using magnetic field lines.

  • Magnetic field lines form closed loops from the North pole to the South pole of a magnet.
  • Field strength is indicated by how close the field lines are; closer lines mean stronger magnetic field.
  • The SI unit of magnetic field strength is the Tesla (T).

⚡ How Electric Current Produces a Magnetic Field

When electric current flows through a conductor, moving charges produce a magnetic field around it. This was first experimentally discovered by Hans Christian Ørsted in 1820 when he noticed that a compass needle deflects near a current-carrying wire.

The magnetic field produced by a current-carrying wire follows the Right-Hand Thumb Rule, which helps to determine the direction of the magnetic field.

🖐️ Right-Hand Thumb Rule (Magnetic Field Direction)

The Right-Hand Thumb Rule states:

Hold the conductor with your right hand such that your thumb points in the direction of the current. Your curled fingers then indicate the direction of the magnetic field lines around the wire.

This rule applies to different conductor shapes such as:

  • Straight wires
  • Coils (circular loops)
  • Solenoids (long coils)
Current (I) Right Hand Thumb Rule Thumb Fingers curl

🌀 Magnetic Field Lines and Their Properties

Magnetic field lines have specific properties that help us understand magnetic effects:

  • They form closed loops without beginning or end.
  • The density of field lines indicates the strength of the magnetic field.
  • They never intersect each other.
  • They emerge from the North Pole and enter the South Pole outside a magnet.

In current-carrying wires, the magnetic field lines form concentric circles around the wire.

🔢 Important Equations

The magnetic field strength (B) depends on the conductor's shape and current (I).

1. Magnetic Field Around a Straight Wire:

B = μ₀ × I⁄2πr

Where,
μ₀ = permeability of free space = 4π × 10-7 T·m/A,
I = current in amperes (A),
r = distance from wire in meters (m).

2. Magnetic Field at Center of Circular Loop:

B = μ₀ × I⁄2R

R = radius of the circular loop (m)

3. Magnetic Field Inside a Solenoid:

B = μ₀ × n × I

n = number of turns per unit length (turns/m)

✋ Fleming’s Left-Hand Rule (Force on Current-Carrying Conductor)

When a current-carrying conductor is placed in an external magnetic field, it experiences a force. The direction of this force is given by Fleming’s Left-Hand Rule.

Stretch your left hand such that the Thumb, Forefinger, and Middle finger are perpendicular to each other:
  • Thumb points in direction of Force (Motion)
  • Forefinger points in direction of Magnetic Field
  • Middle finger points in direction of Current
Thumb
(Force) Middle Finger
(Current) Forefinger
(Magnetic Field) Fleming's Left-Hand Rule

🔧 Real-Life Example: Electric Motor Operation

An electric motor works on the principle of magnetic force acting on a current-carrying conductor inside a magnetic field. When current passes through the coil, the magnetic field created interacts with the permanent magnet's field, producing a force. This force causes the coil to rotate.

  • Current direction: Through the coil wire.
  • Magnetic field: From the permanent magnets.
  • Force direction: Perpendicular to both current and magnetic field — makes the coil spin.
Example: When you turn on a ceiling fan, electric current flows through the motor coils. The magnetic forces acting on the coils make the fan blades rotate and circulate air.

🧩 Applications of Magnetic Field Due to Current

  • Electric Motors: Convert electrical energy to mechanical energy.
  • Generators: Convert mechanical energy to electrical energy by moving coils in magnetic fields.
  • Electromagnets: Created by current in coils, used in cranes, relays, and medical equipment.
  • Transformers: Rely on changing magnetic fields due to alternating current.
  • Magnetic Storage: Hard drives and tape drives use magnetic fields created by currents to store data.

📌 Summary for Students

  • Electric current creates a magnetic field around a conductor.
  • Right-Hand Thumb Rule helps visualize the magnetic field direction around current-carrying wires.
  • Fleming’s Left-Hand Rule determines force direction on a conductor in a magnetic field.
  • These principles are the foundation of many electrical devices like motors and transformers.