The Magnetic Field of a Coil
When a current-carrying coil generates a magnetic field, the strength of this field is determined by several factors, including the number of turns, the current flowing through the coil, and the radius of the coil.
Single Turn Coil
- A circular coil with one turn and current I produces a magnetic field at its center.
- The formula for the magnetic field (B) at the center of a single circular loop is given by:
B = (μ₀ * I) / (2 * R)
where μ₀ is the permeability of free space and R is the radius of the coil.
Smaller Coil with 4 Turns
- When the same wire is wound into a smaller coil with 4 turns, the total length of the wire remains constant, but the radius decreases.
- The magnetic field at the center of this new coil is given by:
B' = (μ₀ * n * I)
where n is the number of turns per unit length. Here, n = 4 turns.
Effect of Increasing Turns
- The total magnetic field at the center of the smaller coil becomes:
B' = (μ₀ * 4 * I) / (2 * r)
where r is the new smaller radius.
Comparison of Magnetic Fields
- Although the smaller coil has more turns, the radius is also smaller, which increases the magnetic field strength considerably.
- The magnetic field strength in the smaller coil will be greater than that in the larger coil due to the increased number of turns, despite the reduced radius.
Conclusion
- Therefore, the magnetic field at the center of the smaller coil with 4 turns will be significantly stronger than that of the single turn coil, showcasing the influence of both the number of turns and the radius on magnetic field strength.