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A circular coil of wire 8.6 $\mathrm{cm}$ in diameter has 15 turns and carries a current of 2.7 $\mathrm{A}$ . The coil is in a region where the magnetic field is 0.56 $\mathrm{T}$ (a) What orientation of the coil gives the maximum torque on the coil, and what is this maximum torque? (b) For what orientation of the coil is the magnitude of the torque 71$\%$ of the maximum found in part (a)?

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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

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

Lectures

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".

04:57

A circular coil of wire 8.…

A wire of length $12.5 \m…

05:14

A wire of length $25.0 \ma…

02:13

A circular coil of 160 tur…

04:09

7ssm The maximum torque ex…

02:27

The maximum torque experie…

03:17

A circular coil of 500 tur…

A rectangular coil $25 \ma…

07:29

A solenoid with 8500 turns…

04:08

\Lambda wire of length 25.…

So here they want us to find the torque on a solenoid. So the torque on its own, the formula for the torque on a solenoid is going to be equal to the number of coils in the solenoid times, the current times, the cross sectional area of the solenoid times, the magnetic field time sign of fi. Now, for part, a specifically sign if I was going to be equal to one so we can say that the torque is going to be equal to 15 coils times 2.7 amperes times the cross sectional area. So pie times 0.0 for three meters squared and then multiplied by 0.56 Tesla's and we find that the torque on the solenoid will be 0.13 to Newton meters. Now, this is actually a Max because we said that thesis I knw if I's going to be equal toe one, which happens to be the greatest value for the sign. If I term so here we're going Tio here. We're trying to find the torque, and subsequently we actually found the maximum torque so prefer be, However, they're saying that the torque is only 71% of its maximum torque, so t so towel rather equals point 71 town max Oh, are the maximum torque. And we're trying to find the angle that the plane of the coil makes with the magnetic field direction. So if we know that tau equals 0.71 of Tell Max and Town Maxes equaling and I ah, the N I A. Time N times eight times a end times I times a times B We know that the on ly term left in this case would be the sign of Fei terms so we can actually make the relationship and say that sign of fire is going to be equal 2.71 given that tower already equals and times I times a times b again. So we can say that fire is going to be simply equal toe arc sine of 0.71 and this is going to equal approximately 45 degrees. So we can say that the clain of the coil makes and angle of 45 degrees with the direction of the magnetic field. And this would be our answer for apart be This would be your answer for a party that is the end of the solution. Thank you for watching

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