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$\cdot$ A solenoid is designed to produce a 0.0279 T magnetic field near its center. It has a radius of 1.40 $\mathrm{cm}$ and a length of $40.0 \mathrm{cm},$ and the wire carries a current of 12.0 A. (a) How many turns must the solenoid have? (b) What total length of wire is required to make this solenoid?

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a) 740 turnsb) 65.06 $\mathrm{m}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 20

Magnetic Field and Magnetic Force

Motion Along a Straight Line

Motion in 2d or 3d

Electric Charge and Electric Field

Gauss's Law

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

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18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

04:28

A magnetic field is a mathematical description of 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. The term "magnetic field" is often used to refer to the B field. In a vacuum, B and H are the same, whereas in a material medium, B is a component of H. In the latter case, H is the "magnetic field strength", and B is the "magnetic flux".

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6. A solenoid is designed …

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So here we have a center of along so annoyed so again, a centre of long songs or eat. And we need to find the, um we're trying to find the magnetic field so we can say that B is going to be equal to mu, not times and times. I I lied about my oh, so here mu not would be the ah magnetic permeability in a vacuum or the primitive ity free space times the number of coils times the ah i the current divided by the length of the solenoid. So this will be equal 24 pine times 10 to the negative. Seventh times, 450 coils times 1.75 meters and then this would be divided by 0.35 meet Sorry, 1.75 amps. My apologies. Divided by a 0.35 meters. And so the magnitude of the magnetic field is going to be a 2.83 times 10 to the negative third Tesla's. So this would be your answer for part for party and then for part B, they're asking us to find the magnetic field of a wire so we can say a distance R from a long St Weir. Ah, this is going to be equal to B equaling knew, not times I. So this would be simply the again. The magnetic permeability, the vacuum times, the current divided by two pi times thie are the distance away from the long straight wire, so this is going to be for pie times 10 to the negative. Seventh times, 1.75 amps divided by two pi times a distance of 0.1 meter. So one centimeter and this is equaling 3.50 times, 10 to the negative. Fifth. Tesla's so again, thie length of the wire, of course, doesn't isn't taken into account because this is a long straight wire. When they say long, they mean infinitely long. So ah, the formula is tailored such that our is denoting again the distance from that wire. So 0.1 meters would be one centimeter away from the wire, and that is the end of the solution. Thank you for watching

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