Moving Charges and Magnetism notes

Moving Charges and Magnetism explains how moving charges and electric currents produce magnetic effects and experience magnetic forces. The chapter begins with magnetic field, Lorentz force and motion of charged particles in uniform magnetic fields, including circular, helical motion and cyclotron. Biot-Savart law calculates magnetic field due to current elements, straight wires and circular loops. Ampere’s law simplifies field calculations for symmetric systems such as long wires, solenoids and toroids. The chapter then studies force on current-carrying conductors and force between parallel currents. Current loops behave like magnetic dipoles and experience torque in magnetic fields. Finally, the moving coil galvanometer uses torque on a current loop to detect current. For NEET, formulas and direction rules are extremely important.

Magnetic force acts on moving charges in a magnetic field. Its vector form is F = q(v × B), so its magnitude is F = qvB sinθ. The force is perpendicular to both velocity and magnetic field, so it cannot change speed or kinetic energy; it only changes direction. If velocity is perpendicular to magnetic field, the particle moves in a circle with radius r = mv/(qB). If velocity has both parallel and perpendicular components, the perpendicular component causes circular motion while the parallel component remains unchanged, producing helical motion. The cyclotron uses repeated acceleration by electric field and circular motion in magnetic field to accelerate charged particles.

Biot-Savart law gives the magnetic field produced by a small current element. The field contribution is proportional to current, length of current element and sine of the angle between current element and position vector, and inversely proportional to square of distance. Its direction is given by the right-hand screw rule or cross product dl × r. This law is used to derive magnetic field due to a straight current-carrying wire and circular current loop. For a long straight wire, B = μ0I/(2πr). At the centre of a circular loop, B = μ0I/(2R), and for N turns it becomes μ0NI/(2R). NEET often asks field magnitude and direction.

Ampere’s circuital law states that the line integral of magnetic field around a closed path equals μ0 times the net current enclosed: ∮B·dl = μ0I. It is especially useful for symmetric current distributions such as an infinite straight wire, long solenoid and toroid. For an infinite straight wire, it gives B = μ0I/(2πr). A solenoid is a long helical coil that produces nearly uniform magnetic field inside and weak field outside; for a long solenoid, B = μ0nI. A toroid is a solenoid bent into a circular ring; its magnetic field is confined mostly inside the core. NEET focuses on field formulas, symmetry and comparison of solenoid and toroid.

A current-carrying conductor placed in a magnetic field experiences force because the moving charges inside it experience magnetic force. For a straight conductor of length L carrying current I in magnetic field B, force is F = BIL sinθ. Direction is given by Fleming’s left-hand rule: first finger for magnetic field, middle finger for current and thumb for force. Two parallel current-carrying wires also exert forces on each other because each wire produces a magnetic field that acts on the other. Parallel currents in the same direction attract, while opposite currents repel. This interaction is used to define the ampere in classical electromagnetism and is frequently tested in NEET.

A current loop behaves like a magnetic dipole. Its magnetic dipole moment is M = IA for one turn and M = NIA for N turns, directed perpendicular to the plane of the loop by the right-hand rule. When placed in a uniform magnetic field, the loop experiences no net force but experiences torque τ = MB sinθ = NIAB sinθ, tending to align its magnetic moment with the field. This principle is used in electric motors and moving coil galvanometers. Torque is generally turning effect of force and also follows τ = rF sinθ, where only the perpendicular component of force produces rotation. Potential energy of a magnetic dipole is U = -M·B = -MB cosθ.

A moving coil galvanometer is an instrument used to detect and measure small currents. It consists of a rectangular coil suspended in a radial magnetic field between concave pole pieces, with a soft iron core to strengthen the field. When current flows through the coil, it experiences magnetic torque τ = NIAB. The suspension fibre provides restoring torque kθ. At equilibrium, NIAB = kθ, so deflection θ is directly proportional to current. This is the principle of the galvanometer. Current sensitivity is deflection per unit current, and voltage sensitivity is deflection per unit voltage. A galvanometer is converted into an ammeter by connecting a low shunt resistance in parallel and into a voltmeter by connecting a high resistance in series.