--- title: "Magnetic Flux, Flux Linkage and Faraday's Law" description: "For a uniform field, flux through a flat loop is B A cos theta, with theta measured from the loop normal. Flux linkage is N times the flux. Signed induced emf is the negative rate of linkage change; i" canonical: https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt source: https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt.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`. # Magnetic Flux, Flux Linkage and Faraday's Law For a uniform field, flux through a flat loop is B A cos theta, with theta measured from the loop normal. Flux linkage is N times the flux. Signed induced emf is the negative rate of linkage change; its magnitude is the absolute value. Subject: Science · Area: Energy · Ages 17 to 18 Page: https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt ## Ready when they can - Calculates flux as BA cos theta and flux linkage as the number of turns times the flux - Finds signed induced emf from the negative gradient of a flux linkage against time graph, and emf magnitude from the gradient's absolute value - Explains why a coil turning in a steady field still has a changing linkage ## Lesson: Magnetic flux and induced emf Induction produces an emf (voltage) when flux linkage changes. In a uniform field, a flat loop has flux B A cos theta. Theta is the angle between field and loop normal, perpendicular to the loop. Flux is in webers: 1 Wb = 1 T m squared. Face on, theta = 0 and cos theta = 1. Edge on, theta = 90 degrees gives zero flux even in a strong field. For N turns sharing the same flux, linkage is N times flux, in weber-turns. Average emf = -(change in flux linkage)/(elapsed time). Instantaneous emf is the negative gradient of a linkage against time graph. An emf's magnitude is its absolute value; a flat line gives zero emf. With fixed reference directions, the minus sign follows Lenz's law: the induced effect opposes the flux change. A straight fall from 10 to 2 weber-turns in 4 s gives gradient (2 - 10)/4 = -2 Wb/s and emf +2 V. A coil turning so that the angle between its normal and a steady field changes has changing flux linkage. Linkage is N B A cos theta; with N, B and A fixed, changing cos theta changes linkage. A rotating-coil generator uses this effect. Faster rotation, more turns, a stronger field or a larger coil area increases the peak emf for this arrangement, with the other quantities fixed. **Recap.** Flux = B A cos theta; linkage = N times flux. Emf is the negative rate of linkage change, and its magnitude is the absolute value. A rotating coil can keep linkage changing. *Original magnetic-flux lesson and questions written for Marble.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Electromagnetic induction and generators](https://lightmysky.com/learn/science/electromagnetic-induction-and-generators-mt_e0jgUKANT-) - [Charged Particles Moving in a Magnetic Field](https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI) ## Opens up - [Lenz's Law and the Alternating-Current Generator](https://lightmysky.com/learn/science/lenzs-law-and-the-alternating-current-generator-mt_69u-fTOSku)