Solution:

1. Apparatus:
   • Magnetic compass
   • Helmholtz coils or solenoid
   • Power supply for Helmholtz coils
   • Protractor or angular measurement device
2. Procedure:
   • Calibrate the Helmholtz coils to produce a known magnetic field.
   • Place the compass at the center of the Helmholtz coils.
   • Adjust the current in the coils until the compass needle is deflected by 45 degrees.
   • Measure the current and calculate the magnetic field produced by the coils.
   • Use the known field from the coils and the deflection angle to calculate the Earth’s magnetic field.
3. Calculations:
   • Use the formula Bearth=Bcoiltan⁡(θ)B_{earth} = B_{coil} \tan(\theta)Bearth​=Bcoil​tan(θ), where BcoilB_{coil}Bcoil​ is the magnetic field produced by the coils, and $\theta$ is the deflection angle.
4. Error Minimization:
   • Ensure accurate calibration of the Helmholtz coils.
   • Use a precise protractor for angular measurements.
   • Perform the experiment away from magnetic disturbances and repeat multiple times for consistency.

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