Experiment to measure the magnetic field of an antenna coil

🎯 Objective

• To measure the magnetic field B inside a solenoid as a function of current I.
• To study the effect of coil length L and number of turns N on the magnetic field.
• To verify the theoretical relation B = μ₀ (N·I / L).

⚙️ Apparatus

• Air coil with adjustable turns.
• High-current power supply.
• Teslameter (measures magnetic field in mT).
• Axial B-probe with Hall sensor.
• Stand for mounting the coil and probe.

📖 Theory

The magnetic field produced by a current-carrying conductor is given by Biot–Savart’s law:

dB = (μ₀ / 4π) * (I · ds × r̂) / r²

For a long solenoid, Ampere’s law gives:

B = μ₀ · (N · I) / L

where μ₀ = 4π × 10⁻⁷ Vs/Am (permeability of free space), N = number of turns, I = current (A), and L = coil length (m).

Part 1 – Magnetic Field vs. Current (B–I Relationship)

🔬 Procedure:

1. Place the air coil on the stand and align the B-probe at the coil’s center.
2. Keep the coil length fixed (e.g., 15 cm) with 30 turns.
3. Connect the coil to the power supply and the teslameter; calibrate to zero.
4. Increase the current gradually (e.g., 0–20 A) and record the magnetic field each time.
5. Reset to zero before each reading to ensure accuracy.

Number of turns (N): Coil length (L) in meters:

Current I (A)	Magnetic Field B (mT)	Action

Part 2 – Magnetic Field vs. Coil Length and Turn Density (B–L and B–n)

🔬 Procedure:

1. Fix the current (e.g., 20 A).
2. Keep total turns constant (N = 30).
3. Adjust the coil length symmetrically between 8 cm and 40 cm.
4. Measure the magnetic field B for each coil length.
5. Calculate turn density n = N / L.
6. Plot B vs. L and B vs. n to observe relations.

Current (I) in A: Number of turns (N):

Coil Length L (cm)	B (mT)	n (turns/cm)	Action