MAGNETIC FIELD DUE TO CIRCULAR COIL WORKING MODEL

MAGNETIC FIELD DUE TO CIRCULAR COIL

The magnetic field produced by a circular coil carrying an electric current can be calculated using Ampère’s Law or the Biot-Savart Law. However, for a circular coil, a simpler approach is often used, which approximates the coil as a series of circular loops, each carrying a current. Here’s an overview:

**Magnetic Field at the Center of a Circular Coil:**
Consider a circular coil with \(N\) turns, each carrying a current \(I\). The magnetic field at the center of the coil (on the axis of the coil) can be calculated using the formula:

[ B = mu_0 N . I / 2R ]

Where:
– \( B \) is the magnitude of the magnetic field at the center of the coil (in teslas, T).
– \( \mu_0 \) is the permeability of free space (4pi  x 10^{-7} Tm/A).
– \( N \) is the number of turns in the coil.
– \( I \) is the current flowing through each turn of the coil (in amperes, A).
– \( R \) is the radius of the circular coil (in meters, m).

**Direction of the Magnetic Field:**
The direction of the magnetic field at the center of the coil is perpendicular to the plane of the coil and follows the right-hand rule. If you wrap your right hand around the coil with your fingers curling in the direction of the current flow (conventional current, from positive to negative), your thumb will point in the direction of the magnetic field lines.

**Characteristics of the Magnetic Field:**
1. **Strength:** The strength of the magnetic field at the center of the coil depends on factors such as the number of turns in the coil, the current flowing through each turn, and the radius of the coil.

2. **Symmetry:** The magnetic field produced by a circular coil is symmetric about the axis of the coil. It forms concentric circles around the axis of the coil.

3. **Dependence on Coil Parameters:** Increasing the number of turns or the current flowing through each turn increases the strength of the magnetic field. Similarly, increasing the radius of the coil also increases the strength of the magnetic field.

**Applications:**
– Circular coils are commonly used in electromagnets, solenoids, and inductors.
– Understanding the magnetic field produced by circular coils is essential in designing and analyzing electrical and electronic devices.

**Teaching Suggestions:**
– Use diagrams and illustrations to demonstrate the magnetic field produced by a circular coil.
– Conduct hands-on experiments with magnetic field sensors or compasses to visualize and measure the magnetic field strength at different points around the coil.
– Encourage students to calculate and predict the strength and direction of the magnetic field using the mathematical formula and the right-hand rule.

Magnetic Field Inside the Circular Coil:

1. Direction:
   • Inside the circular coil, the magnetic field lines run parallel to the axis of the coil.
   • The direction of the magnetic field inside the coil follows the Right Hand Rule: if you curl your fingers in the direction of the current flowing through the coil, your thumb points in the direction of the magnetic field lines inside the coil.
2. Uniformity:
   • The magnetic field inside the circular coil is relatively uniform and strong, especially near the center of the coil.
   • This uniformity arises from the close winding of the wire turns, which results in the magnetic fields produced by individual turns adding up constructively.
3. Strength:
   • The strength of the magnetic field inside the circular coil depends on factors such as the number of turns in the coil, the current flowing through the coil, and the radius of the coil.

Magnetic Field Outside the Circular Coil:

1. Direction:
   • Outside the circular coil, the magnetic field lines form loops around the coil, resembling those of a bar magnet.
   • The direction of the magnetic field outside the coil follows the same pattern as inside, but the field lines spread out and become weaker as they move away from the coil.
2. Extent:
   • The magnetic field outside the circular coil extends a short distance from the sides of the coil and rapidly decreases in strength with increasing distance from the coil.

Applications:

• Circular coils are commonly used in various electromechanical devices, such as electromagnets, solenoids, and inductors.
• They are also used in scientific instruments, medical devices, and industrial machinery for generating controlled magnetic fields and for applications such as magnetic resonance imaging (MRI) and magnetic particle inspection.

Conclusion:

The magnetic field due to a circular coil is an essential aspect of electromagnetism, with applications in a wide range of fields. Understanding the characteristics of the magnetic field inside and outside a circular coil is crucial for designing and analyzing electromagnetic systems and devices.