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An air-filled toroidal solenoid has a mean radius of 15.0 $\mathrm{cm}$ and a cross-sectional area of 5.00 $\mathrm{cm}^{2} .$ When the current is $12.0 \mathrm{A},$ the energy stored is 0.390 $\mathrm{J} .$ How many turns does the winding have?

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2850 turns

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

University of Michigan - Ann Arbor

University of Washington

University of Sheffield

Lectures

03:27

Electromagnetic induction is the production of an electromotive force (emf) across a conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of electromagnetic induction in 1831.

08:42

In physics, a magnetic field is a vector field that describes the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (usually in the cgs system of units) and B is measured in teslas (SI units).

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An air-filled toroidal sol…

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A toroidal solenoid has an…

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A toroidal solenoid has me…

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A toroidal solenoid has 50…

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A solenoid has diameter $2…

So here we have a inducted of a tour or it'll South Seoul annoyed. So we can say l of steroidal so annoyed and this is going to be l equaling mu not and squared times, eh? Divided by two pi r So the magnetic permeability and a vacuum times the number of turns squared times the area divided by two pi r So and we also know the energy stored Ah, and and in Doctor. And this is going to be you so that I'd be stand for energy equalling 1/2 how I squared. So at this point, we can actually see substitute this l in for the energy equation So we can say that Hey, you is going to be equal to, um you not and squared, eh? Times I squared divided by four pi r We kind of thought for the number of turns So we can say that the number of turns is simply going to be equal to the square root of four pi. Are you divided by mu Not, eh? Hi squared. So at this point, we can solve directly, uh, and say that the number of turns equals the square root. So this would be mu not so for pie times 10 to the negative. Seventh time's a so 5.0 times 10 to the negative fourth meters squared Time's thie current of 12 amps squared, and then it will be for pie times the 0.150 meters times the amount of energy. So 0.390 Jules and we're getting that this is going to be equal to 2,850 turns. So this would be our final answer for the number of turns of this toy, or it'll solve annoyed. That is the end of the solution. Thank you for watching.

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