Phys 202 1nd Edition Lecture 16Outline of Last Lecture I. Ampere’s law and Biot-Savart’s lawOutline of Current Lecture II. Review of Ampere’s lawIII. Example problemIV. Electromagnetic InductionCurrent LectureReview of Ampere’s law: According to Ampere’s law, current gives rise to magnetic field. The law states that the integral of B around any closed mathematical path equals µ0 times the current intercepted by the area spanning the path. In other words, if you add up the magnetic field at each point along a certain path encircling your current-carrying wire, then it will equal the amount of current enclosed by this path. This is very similar to Gauss’s law on charges, as Ampere’s law basically applies to the sum of points over a closed loop. This value is called an amperial sum. Ampere’s law is equivalent to Biot-Savart’s law: B=(µ/4π)I(Lr/r3).Example Problem:The rectangular loop shown below, carrying the current I, is located in a uniform magnetic field of 0.35 T pointing in the positive x direction. What is the magnitude of the magnetic dipole moment of the loop? Use the following data: H=7.5cm, W=6.5cm, I=10A, φ=39.5⁰ Z Y φ XMagnetic moment is equal to turns times current times area(N*i*a)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.µ=NIA=(1)(10)(.065*.075) =.049Am2B is along the –x axis. Find the torque: Torque is the agent that causes the magnetic needle to rotate and is equal to the magnetic moment times the magnetic field(µB)T=µB=µBSin(θ) where θ is the angle by which the loop turns(not φ).How we find the value of θ depends on the axis that B runs along:For B along a –x θ=φFor B along a +Y θ=90-φFor B along a –Y θ=90+φSo for this problem, T=µBSin(φ)=(.049)(.35)Sin(39.5)=.011NElectromagnetic induction:The equations and variables used to calculate different aspects of the electric field are applicable towards calculating different aspects of the magnetic field. For example:Q => E => V => ∫E ∙ dlI=Δq/ΔtV=iR => EΔl=iRRemember that current gives rise to a magnetic field, meaning that i=> B => magnetic loop=magnetic needle (Both a magnetic loop and a magnetic needle have one face facing the north pole and the other facing the south pole)If magnetic field is caused by current, then the current and magnetic field experience a force equal to;FB=I(L⨂B)=i|L||B|This gives rise to Faradays law of electromagnetic induction. Basically, this law describes the relationship between an electric circuit and a magnetic field. If there is a rate of change of magnetic flux with respect to time ( ∆ Φ B∆ t) then this change will be equal to the induced potential difference. Since the potential difference over a magnetic loop is represented as ∮E ∙ dl, the equation for Faraday’s law of induction is;∫E ∙ dl=−Δ ΦBΔ tWhere ΦB represents the flux, which is equal to the magnitude of the field times the
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