Lecture Notes on Magnetic Effects of Current

Introduction

• Motivational Quote:
  • "रख हिम्मत एवं मंजर भी आएगा..."
• Lecture Topic: Magnetic Effects of Current
• Topics to Cover Today:
  • Biot-Savart Law
  • Ampere's Circuital Law
  • Magnetic Field due to Moving Coil
  • Galvanometer
  • Sample Paper Questions

Key Concepts

Review of Previous Topics

• Electrostatics: Discussion on properties associated with a charge at rest.
• Current Electricity: Current is defined as the flow of charge.
• Motion of Charge:
  • Rest: Associated with an electric field.
  • Constant Velocity: Associated with both electric and magnetic fields.
  • Acceleration: Produces electromagnetic waves.

Important Laws

• Current-Carrying Wires:
  • A wire carrying current produces a magnetic field around it.
• Biot-Savart Law:
  • Describes the magnetic field produced at a point in space due to a small segment of current-carrying wire.
  • Formula:
    • dB = (μ₀/4π) * (I * dl × r̂) / r²
  • Factors affecting magnetic field: Current element, angle, and distance from the element.

Ampere's Circuital Law

• Statement:
  • Integral of magnetic field (B) over a closed loop is equal to μ₀ times the total current (I) enclosed by the loop.
  • Formula:
    • ∮B • dl = μ₀ * I

Moving Coil Galvanometer

• Principle:
  • A coil placed in a magnetic field experiences torque due to current, resulting in deflection.
• Torque:
  • τ = n * B * I * A * sin(θ)
  • Where n = number of turns, B = magnetic field, I = current, A = area of the coil, θ = angle between B and A.

Sensitivity of Galvanometer

• Current Sensitivity:
  • Defined as the deflection per unit current.
  • Formula:
    • k = α/I
  • Where α is the angle of deflection.
• Voltage Sensitivity:
  • Defined as the deflection per unit voltage.

Applications

Converting Galvanometer to Ammeter or Voltmeter

• To Ammeter:
  • Use a shunt resistance in parallel to keep the current passing through the galvanometer low.
• To Voltmeter:
  • Use a high resistance in series, so the majority of current bypasses the galvanometer.

Example Problems

• Force between two parallel current-carrying wires:
  • F/L = (μ₀/2π) * (I₁ * I₂) / d
  • Where F is the force, L is the length of the wire, and d is the distance between the wires.
• Magnetic field at the center of circular loops:
  • B = (μ₀ * I) / (4 * π * R) for a single loop.

Conclusion

• Key Takeaway:
  • Understanding these principles is crucial for mastering electromagnetic concepts and solving related problems.

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• Next Session: Will cover additional applications and practice problems.