🎯 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.

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.