Physics for Scientists and Engineers 8ed - ch30 - PowerPoint Slides

Physics for Scientists and Engineers 8ed - ch30 - PowerPoint Slides

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 30 Sources of the Magnetic Field Biot-Savart Law Introduction Biot and Savart conducted experiments on the force exerted by an electric current on a nearby magnet They arrived at a mathematical expression that gives the magnetic field at some point in space due to a current Biot-Savart Law Set-Up The magnetic field is at some point P The length element is The wire is carrying a steady current of I Please replace with fig. 30.1 d B r d s r Biot-Savart Law Observations The vector is perpendicular to both and to the unit vector directed from toward P The magnitude of is inversely proportional to r 2 , where r is the distance from to P d B r r d B r d s r d s r d s r Biot-Savart Law Observations, cont The magnitude of is proportional to the current and to the magnitude ds of the length element The magnitude of is proportional to sin , where is the angle between the vectors and d s r r d s r d B r d B r The observations are summarized in the mathematical equation called the Biot-Savart law : The magnetic field described by the law is the field due to the current-carrying conductor Dont confuse this field with a field external to the conductor Biot-Savart Law Equation 2 4 o P d d r = r r I Permeability of Free Space The constant o is called the permeability of free space o = 4 x 10-7 T . m / A Total Magnetic Field is the field created by the current in the length segment ds To find the total field, sum up the contributions from all the current elements I The integral is over the entire current distribution d B r 2 4 o P d r = r r I d s r Biot-Savart Law Final Notes The law is also valid for a current consisting of charges flowing through space represents the length of a small segment of space in which the charges flow For example, this could apply to the electron beam in a TV set d s r Compared to Distance The magnitude of the magnetic field varies as the inverse square of the distance from the source The electric field due to a point charge also varies as the inverse square of the distance from the charge B r E r Compared to , 2 Direction The electric field created by a point charge is radial in direction The magnetic field created by a current element is perpendicular to both the length element and the unit vector r d s r B r E r Compared to , 3 Source An electric field is established by an isolated electric charge The current element that produces a magnetic field must be part of an extended current distribution Therefore you must integrate over the entire current distribution B r E r for a Long, Straight Conductor The thin, straight wire is carrying a constant current Integrating over all the current elements gives ( 29 2 1 1 2 4 4 S o P o P B P dP a P P P a = - =- I cos I sin sin ( 29 sin d dx P = s r k r B r for a Long, Straight...
View Full Document

Page1 / 73

Physics for Scientists and Engineers 8ed - ch30 - PowerPoint Slides

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online