Suppose a power line produces a 6.0 ×10^-4-T peak magnetic field 60 times each second at the loc

step 1 High, around the given power line we can consider the initial magnetic field to be 0 and the pea

Suppose a power line produces a 6.0 ×10^-4-T peak magnetic...

Suppose a power line produces a $6.0 \times 10^{-4}-\mathrm{T}$ peak magnetic field 60 times each second at the location of a neuron brain cell of radius $6.0 \times 10^{-6} \mathrm{m} .$ Estimate the maximum magnitude of the induced emf around the perimeter of this cell during one-half cycle of magnetic field change.

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Key Concepts

Time-Varying Magnetic Fields

Time-varying magnetic fields are those that change in magnitude and/or direction over time. The rate of change of these fields directly influences the rate at which the magnetic flux through a loop changes. In scenarios such as alternating current in power lines, the periodic variation of the magnetic field can be used to determine the induced emf over specific time intervals, such as during half-cycles of the oscillation.

Faraday’s Law of Electromagnetic Induction

Faraday’s law states that an electromotive force (emf) is induced in a closed loop when the magnetic flux through the loop changes in time. It is expressed mathematically as emf = -d?/dt, where ? is the magnetic flux, and the negative sign indicates that the induced emf acts to oppose the change in flux (Lenz’s Law). This principle is fundamental to understanding how time-varying magnetic fields induce currents in circuits.

Magnetic Flux

Magnetic flux represents the total magnetic field passing through a given area and is defined as the product of the magnetic field strength and the perpendicular area through which the field lines pass. In problems involving induced emf, calculating the flux is essential since changes in this flux over time are what drive the induction process according to Faraday’s law.

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