Activity on the Sun, such as solar flares and coronal mass ejections, hurls large numbers of charged particles into space. When the particles reach Earth, they can interfere with communications and the power grid by causing electromagnetic induction. For example, a current of millions of amps (known as the auroral electrojet) that runs approximately 100 km above Earth's surface can be perturbed. The change in the current causes a change in the magnetic field it produces at Earth's surface, which induces an emf along Earth's surface and in the power grid (which is grounded). Induced electric fields as high as 6.0 V/km have been measured. We can model the circuit at Earth's surface as a rectangular loop made up of the power lines completed by a path through the ground beneath. We can treat the magnetic field created by the electrojet as being uniform (but not constant) and parallel to Earth's surface near the surface. Consider a 1.0-km-long stretch of power line that is 5.0 m above the surface of Earth, and assume that the plane of the loop is perpendicular to Earth's surface. If the induced emf in the Earth–power line loop is 9.0 V, at what rate |Δ⁢B/Δ⁢t| must the magnetic field through the loop be changing?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Activity on the Sun, such as solar flares and coronal mass ejections, hurls large numbers of charged particles into space. When the particles reach Earth, they can interfere with communications and the power grid by causing electromagnetic induction. For example, a current of millions of amps (known as the auroral electrojet) that runs approximately 100 km above Earth's surface can be perturbed. The change in the current causes a change in the magnetic field it produces at Earth's surface, which induces an emf along Earth's surface and in the power grid (which is grounded). Induced electric fields as high as 6.0 V/km have been measured.

We can model the circuit at Earth's surface as a rectangular loop made up of the power lines completed by a path through the ground beneath. We can treat the magnetic field created by the electrojet as being uniform (but not constant) and parallel to Earth's surface near the surface. Consider a 1.0-km-long stretch of power line that is 5.0 m above the surface of Earth, and assume that the plane of the loop is perpendicular to Earth's surface.

If the induced emf in the Earth–power line loop is 9.0 V, at what rate |Δ⁢B/Δ⁢t| must the magnetic field through the loop be changing?

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