howard (cah3459) – ohw19 – turner – (56705)1This print-out should have 18 questions.Multiple-choice questions may continue onthe next column or page – fnd all choicesbeFore answering.00110.0 pointsA wire carries a current oFI= 44 A along thex-axis Fromx1=-5 cm tox2=1.6 cm.IxxPy1x2±ind the magnitude oF the resulting mag-netic feld at the pointr= 4 cm on theyaxis.Correct answer: 126.785μT.Explanation:Let :x1=-5 cm,x2.6 cm,andr= 4 cm = 0.04 m.±rom the Biot-Savart Lawd&B=μ04πI d&s×ˆrr2,the magnetic feld at a point From a straightline segment isB=μ0I4π r(cosθ1-cosθ2).In this case,θ1= arctan±y-x1²= arctan³4 cm-(-5 cm)´= 38.6598◦,andθ2= 180◦-arctan±yx2²= 180◦-arctan±4 cm1.6 cm²= 111.801◦,so the resultant magnetic feld isB=μ0I4π d(cosθ1-cosθ2)=μ0(44 A)4π(0.04 m)(cos 38.6598◦-cos 111.801◦)=126.785μT.002 (part 1 of 2) 10.0 pointsImagine a very long, uniForm wire that has alinear mass density oF 0.0033 kg/m and thatencircles the Earth at its equator.Assume the Earth’s magnetic dipole mo-ment is aligned with the Earth’s rotationalaxis. The Earth’s magnetic feld is cylindri-cally symmetric (like an ideal bar magnetic).The acceleration oF gravity is 9.8m/s2andthe magnetic feld oF the earth is 9×10-5T.What is the magnitude oF the current inthe wire that keeps it levitated just above theground?Correct answer: 359.333 A.Explanation:Let :g=9./s2,BEarth×10-5T,andμ=0.0033 kg/m.The Earth’s geographical North pole is a mag-netic South pole andvice versa. The Northpole oF a compass is attracted to the Southmagnetic pole oF the Earth, the place whereSanta Claus lives.The magnetic and gravitational Forces mustbalance. ThereFore, it is necessary to have (Forunit length oF wire)F=IB=μgI=B=(0.0033 kg/m) (9./s2)9×10-5T=359.333 A.
howard (cah3459) – ohw19 – turner – (56705)2003 (part 2 of 2) 10.0 pointsThe current in the wire goes in the1.same direction as the Earth’s spinningmotion (West to East).correct2.opposite direction as the Earth’s spinningmotion (East to West).Explanation:Since the Sun rises in the East, the Earthis turning towards the East and the Earth’sangular velocity is parallel to the Earth’s axis,pointing from South to North.SNvEFBIvEarthThe total force on the wire is zero andthe gravitational force is downward (inward),so the magnetic force must be upward (out-ward).If the current goes from West to East, inthe same direction as the Earth’s spinningmotion,&I×&Bwill be vertically upward (out-ward).004 (part 1 of 2) 10.0 pointsA long, solid cylindrical conductor of radius0.8 m carries a current of 2.4 nA parallel to itsaxis and uniformly distributed over its cross-section. The conductor has a resistivity of0.006 Ω·m.
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