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She then uses a permanent magnet of strength B = 0.5 mT to induce a voltage in the (same) coil. Calculate the expected voltage if she pulls the magnet from the coil in 0.03 seconds.

She then uses a permanent magnet of strength B = 0.5 mT to induce a voltage in the (same) coil. Calculate the expected voltage if she pulls the magnet from the coil in 0.03 seconds.

Principles of Physics: A Calculus-Based Text
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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She then uses a permanent magnet of strength B = 0.5 mT to induce a voltage in the (same) coil.

Calculate the expected voltage if she pulls the magnet from the coil in 0.03 seconds.

a) Expected slope of magnetic field versus current = 95x4x10-7 T.m/A 4.974 x 10-4 T/A HON 2R b) Measured value of slope = 4.5 × 10−4 T/A slopex2R 4.5×10 4T/A×2×0.12m N 95 HO 2x0.12m % error = c) The formula for percentage error between a measured value and a theoretical value is : (measured value - theoretical value) (theoretical value) = 3.62″ × 10−7 T.m/A % error for Ho= x 100% (3.62ñ×10¯7T.m/A — 4ñ×10¯7T.m/A) (47x10-7T.m/A) x 100% = 9.5%
Transcribed Image Text:a) Expected slope of magnetic field versus current = 95x4x10-7 T.m/A 4.974 x 10-4 T/A HON 2R b) Measured value of slope = 4.5 × 10−4 T/A slopex2R 4.5×10 4T/A×2×0.12m N 95 HO 2x0.12m % error = c) The formula for percentage error between a measured value and a theoretical value is : (measured value - theoretical value) (theoretical value) = 3.62″ × 10−7 T.m/A % error for Ho= x 100% (3.62ñ×10¯7T.m/A — 4ñ×10¯7T.m/A) (47x10-7T.m/A) x 100% = 9.5%
MAGNETIC FIELDS SUMMARY Solenoids are cylindrical windings of wire. Currents through solenoids create magnetic fields inside that are uniform (in the case of a perfect solenoid) and directed along the axis of the solenoid. In this lab the field at the center of a solenoid will be measured, and from the results the vacuum permeability constant μ, will be calculated. You will then induce a voltage in a coil using a handheld magnet, and from the result determine the strength of the magnet's magnetic field. THEORY The magnetic field B at the center of a circular coil (solenoid) of radius R with N turns that carries a current I is Bcenter Ho NI 2R (1) where μ, is the vacuum permeability constant, μ = 4 x 10-7 T-m /A. The magnetic field at the center is 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 the magnetic flux inside the coil. One way to do this is to change the magnetic field at the center of the coil, 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, , is V=- (2) do dt The 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 becomes approximately AB V = NA At (4) where N is the number of times the wire is wound around the coil, A is the area of the coil, AB is the maximum field produced by the magnet, and At is the time required to move the magnet through the coil. This equation is called Faraday's Law. REFERENCE Cutnell and Johnson Chapter 21. COLOR-KEY This 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.
Transcribed Image Text:MAGNETIC FIELDS SUMMARY Solenoids are cylindrical windings of wire. Currents through solenoids create magnetic fields inside that are uniform (in the case of a perfect solenoid) and directed along the axis of the solenoid. In this lab the field at the center of a solenoid will be measured, and from the results the vacuum permeability constant μ, will be calculated. You will then induce a voltage in a coil using a handheld magnet, and from the result determine the strength of the magnet's magnetic field. THEORY The magnetic field B at the center of a circular coil (solenoid) of radius R with N turns that carries a current I is Bcenter Ho NI 2R (1) where μ, is the vacuum permeability constant, μ = 4 x 10-7 T-m /A. The magnetic field at the center is 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 the magnetic flux inside the coil. One way to do this is to change the magnetic field at the center of the coil, 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, , is V=- (2) do dt The 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 becomes approximately AB V = NA At (4) where N is the number of times the wire is wound around the coil, A is the area of the coil, AB is the maximum field produced by the magnet, and At is the time required to move the magnet through the coil. This equation is called Faraday's Law. REFERENCE Cutnell and Johnson Chapter 21. COLOR-KEY This 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.
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