What is magnetic field due to a circular loop?

Short Answer

The magnetic field due to a circular loop is the magnetic field produced when electric current flows through a circular-shaped wire. This field forms curved lines around the loop, and at the center of the loop, the magnetic field is strong and almost straight.

The direction of the magnetic field can be found using the right-hand thumb rule. The magnetic field strength increases when the current is larger or when the loop has more turns. Circular loops are used in electromagnets, coils, motors, and scientific instruments.

Detailed Explanation

Magnetic field due to a circular loop

When electric current flows through a circular loop of wire, it produces a magnetic field around the loop. This magnetic field is created because moving charges generate magnetic effects. Unlike a straight conductor, where the field forms simple circular lines around the wire, a circular loop produces a more complex pattern. At the center of the loop, the magnetic field lines are nearly straight, parallel, and concentrated. This makes the center of the loop an important region where the magnetic field is strong and uniform.

Understanding the magnetic field due to a circular loop is important in electromagnetism because it forms the basis for many devices such as coils, solenoids, electromagnets, motors, and generators.

Why a circular loop produces a magnetic field

Electric current consists of moving charges. When these charges move along a circular path, each small part of the wire produces its own magnetic field. According to Biot–Savart Law, all these small magnetic fields combine to form the overall magnetic field around the loop.

  • At the center of the loop, all magnetic field components add up in the same direction, making the field strong.
  • At points along the axis of the loop, the field decreases gradually.
  • Outside the loop, the field becomes weaker and more spread out.

The combined effect forms a characteristic magnetic field pattern.

Direction of the magnetic field

The direction of the magnetic field due to a circular loop is given by the right-hand thumb rule:

  • Curl the fingers of your right hand in the direction of the current in the loop.
  • Your thumb points in the direction of the magnetic field at the center of the loop.

Thus:

  • If current flows clockwise, the magnetic field at the center goes downwards.
  • If current flows anticlockwise, the magnetic field at the center goes upwards.

Magnetic field at the center of a circular loop

The magnetic field at the center is given by the formula:

B = μ₀ I / (2R)

Where:

  • B = magnetic field
  • μ₀ = permeability of free space
  • I = current
  • R = radius of the loop

This shows:

  • Larger current → stronger magnetic field
  • Smaller radius → stronger magnetic field

If the loop has N turns, the field becomes:

B = μ₀ N I / (2R)

More turns increase the strength of the magnetic field.

Nature of magnetic field around the loop

  1. Inside the loop (especially center)
    Magnetic field lines are dense, straight, and concentrated.
  2. Along the axis of the loop
    Field weakens as we move away from the center.
  3. Outside the loop
    Field lines spread out and become weaker.
  4. Around the wire
    Circular magnetic field lines form like those around a straight conductor.

Field lines in a circular loop

The pattern of magnetic field lines is as follows:

  • Lines pass straight through the center
  • Then they curve and return to the loop
  • Outside the loop, the lines spread apart
  • The pattern resembles the field of a small magnetic dipole

This makes the circular loop act like a small magnet.

Factors affecting magnetic field of circular loop

  1. Current (I)
    Higher current means stronger field.
  2. Radius (R)
    Smaller radius means stronger field at the center.
  3. Number of turns (N)
    More turns produce a stronger field.
  4. Medium around the loop
    Using a magnetic core increases the field strength.

Applications of circular loops

Circular loops are used in many devices because they produce controllable magnetic fields.

  1. Electromagnets

Coils of wire act as strong magnets when current flows.

  1. Motors and generators

Rotating coils in magnetic fields produce motion or electricity.

  1. Speakers and microphones

Magnetic fields from loops help produce sound.

  1. Magnetic resonance imaging (MRI)

Uses magnetic fields from loops and coils for medical imaging.

  1. Induction cookers

Use magnetic fields from coils to heat objects.

  1. Transformers

Coils act as primary and secondary loops.

Comparison with straight conductor (simple explanation)

  • A straight conductor produces only circular magnetic lines around the wire.
  • A circular loop produces a concentrated magnetic field at the center.

This makes loops more suitable for creating strong magnetic fields in a small space.

Connection to solenoids and toroids

Solenoids and toroids are formed by combining many circular loops:

  • Solenoid → many loops arranged in a line
    Creates a strong uniform field.
  • Toroid → loops bent into a circle
    Magnetic field is confined inside the ring.

Thus, circular loops form the basis of most magnetic devices.

Conclusion

The magnetic field due to a circular loop is the magnetic field created when current flows through a circular wire. The field is strongest and nearly uniform at the center of the loop. Its direction is given by the right-hand thumb rule. The strength depends on current, radius, and number of turns. Circular loops are essential in electromagnets, solenoids, transformers, motors, and many electrical devices. Understanding this concept helps explain how magnetic fields are produced and used in technology.