Magnetism, induction and alternating
Magnets and magnetic fields
A magnetic field describes the magnetic influence at a position. A compass can indicate its direction, while iron filings suggest a pattern rather than literal physical strings. Outside a bar magnet, the field direction is conventionally from north to south; the complete field forms closed patterns. Like poles repel and unlike poles attract. Cutting a bar magnet produces smaller magnets with both poles, not an isolated north pole and south pole. Materials respond differently: soft iron is readily magnetised and demagnetised, whereas suitable permanent-magnet materials retain magnetisation more strongly. A useful application answer links the material property to the device's purpose.
produces a field
A straight -carrying wire has a surrounding magnetic field with circular direction. A right-hand grip convention connects conventional direction with the field direction. Reversing the reverses the pattern. A coil or solenoid combines contributions from its turns and can produce a strong, approximately uniform field in its central region. More turns per unit length, greater and an appropriate ferromagnetic core can increase that field. An electromagnet is useful where magnetism must be controlled electrically. Do not confuse an electron's direction of motion with conventional : their directions in a metal are opposite.
Forces on wires and moving charges
A straight wire of length L carrying I in a uniform field B experiences magnitude, where θ is the angle between and field. is zero for parallel directions and maximum for perpendicular ones. Magnetic flux B is measured in teslas. A moving charge experiences. The is perpendicular to both its motion and the field, with the direction reversed for negative charge. The magnetic alone changes direction, not the or kinetic , of a freely moving point charge because it is perpendicular to at each instant.
Motor action and circular paths
Two opposite sides of a -carrying coil can experience forces producing a turning effect. A simple DC motor uses a split-ring commutator to reverse coil at appropriate stages and maintain the turning tendency. A generator's slip rings or commutator have different output roles, so identify the actual diagram. For a charged particle moving perpendicular to a uniform magnetic field, equate magnetic to centripetal : |q|vB = mv²/r. Then. A larger gives a larger radius; a stronger field gives a smaller radius. The source of in a motor remains the electrical .
Flux is not simply field strength
Magnetic flux through a flat surface in a uniform field is, where θ is measured between the field and the surface normal. A surface perpendicular to the field has maximum flux, because its normal is parallel to the field. Turning it until its plane is parallel to the field gives zero flux. Flux is measured in webers. Flux linkage for N similar turns is NΦ. Changes can arise from B, area, orientation or the portion of the surface within the field. Draw the normal explicitly to avoid using the angle with the plane in the cosine formula.
Faraday and Lenz explain induction
An induced electromotive occurs when magnetic flux linkage changes. Its average magnitude is N|ΔΦ|/Δt for identical turns. A faster change gives a larger average induced emf. The negative sign in the signed form expresses Lenz's law: the induced effect opposes the change that causes it. If a magnet approaches a coil, the induced field opposes the increasing flux, rather than merely opposing the original field in every situation. If the magnet retreats, the induced polarity changes. An emf can exist across an open circuit even though no sustained flows. Mechanical work is required to maintain motion against the induced interaction when is transferred.
Generators and conservation
A rotating coil in a magnetic field changes flux linkage periodically and can generate an alternating emf. Greater rotation rate, field strength, turn count or coil area can increase the peak emf in the ideal model. A generator converts mechanical into electrical ; it does not manufacture without an input. Turbines, engines or other mechanisms the mechanical work. Real devices have , and heating losses. Lenz's law helps explain why drawing useful electrical creates a resisting mechanical load. Describe the chain as well as the changing-field mechanism when answering an application question.
Transformers require changing flux
A transformer couples primary and secondary windings through changing magnetic flux. For an ideal transformer, and. A step-up transformer raises and lowers at the same transferred ; a step-down transformer does the reverse. A steady DC input does not provide continuous transformer action after the switching transient. Real transformers have winding heating, eddy- and hysteresis losses, as well as imperfect flux coupling. Laminating a core reduces eddy currents; suitable core material reduces magnetisation losses. Never infer that higher secondary means higher in an ideal transformer.
Alternating- measurements
A sinusoidal reverses direction periodically. f is cycles per second and period. Its peak value is different from its root--square value. For a sine wave, Irms = Ipeak/√2 and Vrms = Vpeak/√2. RMS gives the equivalent DC heating effect in a resistor. These sine-wave relationships should not be assumed for every waveform. In a purely resistive AC circuit, and are in phase and average is VrmsIrms. The average over a full symmetric sine cycle is zero, yet the heating is positive because depends on squared.
Reactance, impedance and resonance
An inductor opposes changes in , giving inductive reactance. A capacitor's reactance is. Increasing raises XL and lowers XC. For an ideal series RLC circuit, impedance magnitude is. is Vrms/Z. At series resonance, giving minimum impedance R in that ideal circuit. Average real is VrmsIrms cos φ, where cos φ is the factor. These quantities describe a stated sinusoidal steady-state model; switching behaviour and real-component losses require further analysis.
Build a reliable solution
Start by identifying whether a question concerns , flux, induced emf, transformer ratios or AC response. Their symbols can overlap, so define them and keep units visible. For a 200-turn coil whose flux per turn falls by 0.003 Wb in 0.10 s, the average emf magnitude is 6 V. For an ideal 240 V transformer with 1,000 primary and 100 secondary turns, the output is 24 V. If it supplies 120 W, secondary is 5 A and primary is 0.5 A. These are numerical models, not instructions for constructing or testing mains equipment.