# SJSU EE 140 - ch28_B_field (73 pages)

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## ch28_B_field

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- Pages:
- 73
- School:
- San Jose State University
- Course:
- Ee 140 - Principles of Electromagnetic Fields

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Chapter 28 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 r The magnetic field is dB at some point P The length element is r ds The wire is carrying a steady current of I Please replace with fig 30 1 Biot Savart Law Observations r r ds The vector dB is perpendicular to both and r ds to the unit vector r directed from toward P r The magnitude of dB is inversely proportional r to r2 where r is the distance from ds to P Biot Savart Law Observations cont r The magnitude of dB is proportional to the current andr to the magnitude ds of the length element ds r The magnitude of dB is proportional to sin r where is the angle between the vectors ds and r Biot Savart Law Equation The observations are summarized in the mathematical equation called the Biot Savart law r I dsr r dB o 4 r 2 The magnetic field described by the law is the field due to the current carrying conductor Don t confuse this field with a field external to the conductor 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 r dB is the field created by the current in the length segment ds To find the total field sum up the r contributions from all the current elements I ds r I dsr r B o 2 4 r The integral is over the entire current distribution Biot Savart Law Final Notes The law is also valid for a current consisting of charges flowing through space r ds 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 r r B Compared to E 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

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