Class-12th Ch-4(Moving Charges and Magnetism)

Here’s an upgraded, more detailed overview of Chapter 4 – Moving Charges & Magnetism, aligned with NCERT concepts and enhanced for clarity:

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1. Magnetic Field & Oersted’s Discovery

A magnetic field (B) exists around moving charges or currents—its presence can be detected, e.g., by compass needles around a current‑carrying wire. Danish physicist Hans Christian Oersted first demonstrated this in 1820.

2. Lorentz Force on a Moving Charge

A charged particle q moving with velocity v in a magnetic field B experiences a force:
F = q v × B = q vB sinθ,
where θ is the angle between v and B.

• If θ=0° (parallel), F=0.

• If θ=90° (perpendicular), F is maximal.
  Direction is given by the right-hand rule; this force does no work—only changes the direction of motion. 

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3. Motion in Magnetic Fields

Depending on velocity orientation, motion can be:

• Circular (v ⟂ B): radius r = mv/(qB), period T = 2πm/(qB), frequency f = qB/(2πm).

• Helical (v with parallel and perpendicular components): a spiral path.

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4. Magnetic Field from Currents – Biot–Savart Law

A tiny current element I dl generates a magnetic field at P:
dB = (μ₀/4π)·(I dl × r̂)/r²,
integrated along the conductor. 

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5. Field in Specific Configurations

• Long straight wire: B = μ₀I/(2πr) at distance r.

• Circular coil: at center, B = μ₀ nI/(2R) for N turns (n=N total turns); general axial field when far from coil B = μ₀ nI A/(2πx³).

• Solenoid (long coil): inside B = μ₀ nI; at ends B = (1/2)μ₀ nI.

• Toroid: inside B = μ₀ nI; zero outside.

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6. Ampère’s Circuital Law & Displacement Current

∮ B·dl = μ₀ I_enclosed around closed loop.
Ampère’s law computes fields in symmetries (e.g., wire, solenoid), and Maxwell’s addition of displacement current filled the gap when fields change in capacitors.

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7. Force on Current-Carrying Conductors

A conductor of length l carrying current I in a magnetic field B feels force:
F = I l × B, with magnitude I l B sinθ.
Parallel conductors exert magnetic forces:

• Attraction if currents are parallel: F/L = μ₀ I₁ I₂/(2πr)

• Repulsion if antiparallel. 

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8. Torque on Current Loops & Moving‑Coil Galvanometer

A loop in a magnetic field experiences torque τ = nIBA sinφ, where φ is the angle between loop normal and B.
This principle is applied in galvanometers—measuring current via coil deflection.

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9. Cyclotron

A cyclotron accelerates charged particles using a constant magnetic field and alternating electric field.
Particles spiral outward, gaining energy per half-turn as governed by r and T = 2πm/(qB)—independent of speed. 

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10. Conceptual Links & SI Units

• Magnetic field B is measured in tesla (T) (1 T = 1 N/(A·m)).

• Biot–Savart and Ampère’s laws parallel Coulomb’s and Gauss’s laws in electrostatics.

• Maxwell unified electricity, magnetism, optics—all interlinked.

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📚 Formula Summary

Phenomenon	Formula
Force on moving charge	F = qvB sinθ
Magnetic field (wire)	B = μ₀I/(2πr)
Field (coil center)	B = μ₀nI/(2R)
Field (solenoid)	B = μ₀nI
Force on wire	F = I l B sinθ
Circular motion radius	r = mv/(qB)
Cyclotron period	T = 2πm/(qB)

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Why This Chapter Matters

Understanding how electricity and magnetism interrelate is essential for:

• Electric motors, generators, and transformers

• Particle accelerators and beam physics

• Magnetic storage, sensors, and medical imaging (MRI)

• Fundamental electromagnetism and Maxwell’s equations

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Let me know if you want derivations, problem examples, or applications—happy to dive deeper!