--- title: "Lenz's Law and the Alternating-Current Generator" description: "An induced emf has the direction that opposes the change in magnetic flux. In a closed resistive coil it drives a current with that effect. An ideal planar coil rotating at constant angular speed abou" canonical: https://lightmysky.com/learn/science/lenzs-law-and-the-alternating-current-generator-mt_69u-fTOSku source: https://lightmysky.com/learn/science/lenzs-law-and-the-alternating-current-generator-mt_69u-fTOSku.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Lenz's Law and the Alternating-Current Generator An induced emf has the direction that opposes the change in magnetic flux. In a closed resistive coil it drives a current with that effect. An ideal planar coil rotating at constant angular speed about an axis in its plane and perpendicular to a uniform magnetic field produces a sinusoidal emf. Subject: Science · Area: Energy · Ages 17 to 18 Page: https://lightmysky.com/learn/science/lenzs-law-and-the-alternating-current-generator-mt_69u-fTOSku ## Ready when they can - Predicts the direction of an induced current and names the change it opposes - Argues that the opposite sign would let a machine make energy from nothing - Relates the peak emf and the frequency of a generator output to how the coil is turning ## Lesson: Fighting change, spinning power Faraday's law gives the emf from changing flux linkage. Lenz's law gives its direction. Push a north pole toward a closed resistive coil: its near face becomes north, opposing the approach. Viewed from the magnet, the conventional current is counterclockwise. Curl your right fingers with the current; your thumb points toward the coil's north face. With a resistive load, moving the magnet requires work against the induced magnetic force. That work supplies electrical energy and heat. If induction helped the motion while supplying electrical energy, the system could gain energy without an input. The minus sign in Faraday's law expresses this opposition. For an ideal AC generator, a planar coil rotates at constant angular speed omega about an axis in its plane and perpendicular to uniform B. N is the turn count and A is the area. With its normal along B at t = 0, linkage is N B A cos(omega t). The derivative is the graph slope: d cos(omega t)/dt = -omega sin(omega t). Faraday's minus sign gives emf N B A omega sin(omega t). One revolution gives one cycle, so f = omega / (2 pi). For steady rotation with the axis in the coil plane and perpendicular to uniform B, peak emf is N B A omega. Increasing any one factor while holding the others fixed raises the peak. N counts the coil's turns, not its revolutions per second. Increasing N raises the peak but does not change the frequency when the rotation rate is fixed. Now withdraw the north pole from the same closed resistive coil. The magnetic flux decreases. The near face becomes south and attracts the departing north pole, opposing its withdrawal. Viewed from the magnet, the conventional current is clockwise. Induction opposes the change in flux, not always the existing field. Keep the rotation axis in the coil plane and perpendicular to uniform B. If the constant angular speed doubles between two steady runs while N, A and B stay fixed, f = omega / (2 pi) doubles and peak emf N B A omega doubles. The cycles take half as long. These relations describe induced emf; the load's properties also affect current. *(drawing: In a resistive coil with no other supply, any earlier current dies away. Constant linkage then produces no induced current.)* **Recap.** For steady rotation with the axis in the coil plane and perpendicular to uniform B, peak emf is N B A omega and f = omega/(2 pi). Lenz's law gives direction; constant linkage gives zero induced emf. *Original lesson, questions and flashcards authored for this learning dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Magnetic Flux, Flux Linkage and Faraday's Law](https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt) ## Optional connections - [Transformers and the National Grid](https://lightmysky.com/learn/science/transformers-and-the-national-grid-mt_ExV4Kc_7_P) ## Opens up - [Induced Electric Fields and Motional EMF](https://lightmysky.com/learn/science/induced-electric-fields-and-motional-emf-mt_LpmHnz46tu)