AP Physics ST Biot-Savart Law tutornext.com

Biot-Savart Law Shortly after Oersted discovered connection between a current-carrying wire and a magnetic field Jean-Baptiste Biot and Felix Savart began relating magnetic force and current. Their observations are collectively referred to as the Biot-Savart Law. nndb.com ulike.net

Biot-Savart Law 1819 – Oersted – Established the fact that a current-carrying wire (I-wire) produced a magnetic field. – Direction of the magnetic field determined by the Right Hand Rule (RHR) Thumb points in the direction of the current Fingers curl in the direction of the magnetic field. boguta.phy.uic.edu

Biot-Savart Law sdsu-physics.org

Biot-Savart Law Experimental observations: – dB perpendicular to ds and r-hat; r-hat directed from ds to point P – dB (magnitude) is inversely proportional to the square of r; distance from ds to point P – dB (magnitude) is directly proportional to the current I – dB (magnitude) is directly proportional to the magnitude of length element ds – dB is directly proportional to the sinθ; θ = angle between the vectors ds and r-hat

Biot-Savart Law Biot-Savart Law… = permeability of free space

Biot-Savart Law Note - – dB = field created by a small length element of ds. – TOTAL magnetic field (B) at some point requires all current element contributions Ids… meaning integrate!

Coulomb’s Law vs. Biot-Savart Law “Similar yet different” Coulomb’s Law… Biot-Savart Law…

Coulomb’s Law vs. Biot-Savart Law Coulomb – Point charge produces electric field – Electric field varies inversely proportional to the square of the distance separating q 1 and q 2 – Direction of E is radial (perpendicular) to point charge Biot-Savart – Current element produces magnetic field – Magnetic field varies inversely proportional to the square of the distance separating Ids and point P – Direction of B is perpendicular to Ids and r-hat

Coulomb’s Law vs. Biot-Savart Law Coulomb – Electric field is fundamentally established by an isolated point charge Biot-Savart – Magnetic field established by an isolated current element* * current element however can not exist without a complete circuit to provide environment for charge to flow

Lesson Summary

EXAMPLE #1 Magnetic Field Surrounding a Thin, Straight Conductor Consider a thin, straight wire carrying a constant current I and placed along the x axis as shown at right. Determine the magnitude and direction of the magnetic field at point P due to this current. P O x θ dsds r a y x I

EXAMPLE #2 Problem 30-8 A conductor consists of a circular loop of radius R and two straight, long sections, as shown. The wire lies in the plane of the paper and carries a current I. Determine the magnitude and direction of the magnetic field at the center of the loop. I = 7 A R

EXAMPLE #3 Magnetic field on the Axis of a Circular Current Loop Consider a circular wire loop of radius R located in the yz plane and carrying a steady current I. Calculate the magnetic field at an axial point P a distance x from the center of the loop. dBdB dBydBy dBxdBx dsds r x y z x R θ θ I

EXAMPLE #4 Magnetic Field Due to a Curved Wire Segment Calculate the magnetic field at point O for the current- carrying segment. The wire consists of two straight portions and circular arc of radius R, which subtends an angle π/2. The arrow heads on the wire indicate the direction of the current. R ds I I θ O I