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Chapter 4: Moving Charges and Magnetism

Master Moving Charges and Magnetism with NCERT solutions for magnetic fields, Lorentz force, Biot-Savart law, and Ampere's law.

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Quick Revision: Electric Charges and Field

  • Magnetic Field (B): Field produced by moving charges; SI unit tesla (T).
  • Biot-Savart Law: dB = (μ₀/4π) × (Idl × r̂)/r²; magnetic field due to current element.
  • Magnetic Field due to Straight Wire: B = (μ₀I)/(2πr); inversely proportional to distance.
  • Magnetic Field at Center of Circular Loop: B = (μ₀I)/(2R); along axis direction.
  • Ampere's Circuital Law: ∮B·dl = μ₀I_enclosed; relates magnetic field to enclosed current.
  • Magnetic Field due to Solenoid: B = μ₀nI; uniform inside long solenoid.
  • Magnetic Field due to Toroid: B = (μ₀NI)/(2πr); inside toroidal coil.
  • Force on Moving Charge: F = q(v × B); Lorentz force perpendicular to both v and B.
  • Force on Current-Carrying Conductor: F = I(l × B); force on wire in magnetic field.
  • Motion of Charged Particle: Circular path in perpendicular B field; radius r = mv/(qB).
  • Cyclotron: Particle accelerator using crossed E and B fields; frequency f = qB/(2πm).
  • Magnetic Moment: m = IA; for current loop with SI unit A·m².
  • Torque on Current Loop: τ = m × B = mB sinθ; tends to align m with B.
  • Moving Coil Galvanometer: I = (k/NAB)θ; current proportional to deflection.
  • Current Sensitivity: θ/I = NAB/k; deflection per unit current.
  • Voltage Sensitivity: θ/V = NAB/(kR); deflection per unit voltage.
  • Conversion to Ammeter: Shunt resistance S = (I_gG)/(I - I_g).
  • Conversion to Voltmeter: Series resistance R = (V/I_g) - G.
  • Permeability of Free Space: μ₀ = 4π × 10⁻⁷ T·m/A.

Chapter Summary:

Moving Charges and Magnetism explores the fundamental relationship between electric currents and magnetic fields, establishing that moving charges are the source of all magnetic phenomena. The chapter begins with the Biot-Savart law, which provides the mathematical foundation for calculating magnetic fields produced by various current configurations.

Key applications include calculating magnetic fields due to straight conductors, circular loops, solenoids, and toroids. Ampere's circuital law offers an alternative method for determining magnetic fields in symmetric current distributions, analogous to Gauss's law in electrostatics. The chapter then examines the forces experienced by moving charges and current-carrying conductors in magnetic fields, described by the Lorentz force law.

The motion of charged particles in magnetic fields is analyzed, leading to important applications like the cyclotron particle accelerator. Magnetic dipole moments of current loops and the torque experienced by them in magnetic fields are studied in detail. Practical instruments like the moving coil galvanometer are explained, along with their conversion to ammeters and voltmeters for various measurement ranges.

This chapter bridges electricity and magnetism, laying the conceptual groundwork for electromagnetic induction and completing the picture of how electric currents produce magnetic fields and how these fields in turn affect moving charges.