MAGNETIC FIELDSSUMMARYSolenoids are cylindrical windings of wire. Currents through solenoids create magnetic fields insidethat are uniform (in the case of a perfect solenoid) and directed along the axis of the solenoid. In thislab the field at the center of a solenoid will be measured, and from the results the vacuum permeabilityconstant μ, will be calculated. You will then induce a voltage in a coil using a handheld magnet, andfrom the result determine the strength of the magnet's magnetic field.THEORYThe magnetic field B at the center of a circular coil (solenoid) of radius R with N turns that carries acurrent I isBcenterHo NI2R(1)where μ, is the vacuum permeability constant, μ = 4 x 10-7 T-m /A. The magnetic field at the centeris directed along the axis of the solenoid and mostly uniform.Instead of a current creating a magnetic field inside the coil, a current can be induced by changing themagnetic flux inside the coil. One way to do this is to change the magnetic field at the center of thecoil, such as by moving a magnet into (or out of) the solenoid.The voltage magnitude V induced in a single-turn coil by a changing magnetic flux, , isV=-(2)dodtThe flux, Þ, for a single loop of wire perpendicular to a magnetic field B is= BA(3)where A is the area of the loop, A=TR².If the flux through a coil of wire is changed by moving a magnet through it, then equation 2 becomesapproximatelyABV = NAAt(4)where N is the number of times the wire is wound around the coil, A is the area of the coil, AB is themaximum field produced by the magnet, and At is the time required to move the magnet through thecoil. This equation is called Faraday's Law.REFERENCECutnell and Johnson Chapter 21.COLOR-KEYThis document uses colored text to highlight areas of specific importance.Green text highlights commentary to help you understand the lab or how to write your report.Blue text highlights key steps of the lab process that you should read carefully.Red text highlights steps important to your lab data. 1. A student uses a coil of radius 12 cm with 95 windings.a) Calculate the expected slope for a plot of magnetic field vs current in this coil.b) She performs the lab and measures a slope of 4.5 x 104 T/A. Based on this slope, what valuedoes she calculate for μ.?c) Calculate the percent error between her measured value of μo and the theoretical value.

Given, Radius, R = 12 cm = 0.12 mNumber of turns, N = 95 Bcenter =μ0NI2R μ0 = 4π×10-7 T.m/A

1. A student uses a coil of radius 12 cm with 95 windings. a) Calculate the expected slope for a plot of magnetic field vs current in this coil. b) She performs the lab and measures a slope of 4.5 x 104 T/A. Based on this slope, what value does she calculate for μ.? c) Calculate the percent error between her measured value of μo and the theoretical value.

1. A student uses a coil of radius 12 cm with 95 windings. a) Calculate the expected slope for a plot of magnetic field vs current in this coil. b) She performs the lab and measures a slope of 4.5 x 104 T/A. Based on this slope, what value does she calculate for μ.? c) Calculate the percent error between her measured value of μo and the theoretical value.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 25P

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