Lecture on Electromagnetism and Ampère's Law

Overview

• Biot-Savart's Law: Describes the magnetic field (B) generated by a current (I) at a distance R.
  • Formula: ( B = \frac{\mu_0 I}{2\pi R} )
  • Magnetic field is tangential to a circle centered on the wire.

Ampère's Law

• The integral of B around a closed loop equals ( \mu_0 I ) (current enclosed by the loop).
• Ampère's Law can be applied to any closed path, not just circular ones.
• Current "enclosed" concept replaced by "penetration" through a surface attached to the loop.

Application of Ampère's Law

• Outside a wire: For radius ( r > R ), ( B = \frac{\mu_0 I}{2\pi r} ).
• Inside a wire: For radius ( r < R ), ( B = \frac{\mu_0 I r}{2\pi R^2} ) (linearly grows with r).
  • Uniform current density assumption
  • Confirms continuity of magnetic field at surface of the wire.

Solenoids

• Solenoids: Tightly wound spiral wires that create nearly uniform magnetic fields inside.
• Approximation: Magnetic field inside a tightly wound solenoid is constant, very weak outside.
• Magnetic Field Calculation:
  • Assuming ( N ) windings, solenoid length ( L ):
  • ( B = \frac{\mu_0 I N}{L} )
• Numerical Example:
  • Solenoid with 2800 windings, ( L = 0.6 ) meters, and current ( I \approx 4.5 ) amperes results in ( B \approx 0.026 ) Tesla.

Kelvin Water Dropper

• An electrostatic generator using water drops and induced polarization to build up charge.
• Mechanism: Random charge initiates polarization, creating a feedback loop that generates high voltages.
• Role of Gravity: Conducts the process against the electric field's natural direction.
• Practical Demonstration: Water drops spread out due to polarization.

Demonstrations

• Probes and experiments to visualize magnetic field configurations around solenoids and the Kelvin Water Dropper.
  • Use of iron filings to show field lines.
  • Measurements of magnetic field strength using Hall probes.
  • Display of the Kelvin Water Dropper's operation and sparking.

Conclusion

• Ampère's Law offers a powerful tool for calculating magnetic fields in various configurations.
• The Kelvin Water Dropper demonstrates practical uses of electromagnetic principles.