University of Pittsburgh x The B d N WWW.saplinglearning com /ibiscms/mod/ibis/v

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University of Pittsburgh x The B d N WWW.saplinglearning com /ibiscms/mod/ibis/view.php?id 2610233 nu calculator PerioaIC Taol 00 Qu 7 of 10 When a diamagnetic object is placed near one pole of a strong magnet, the object is repelled away from Map 00 the pole by a magnetic force. If the magnet were held vertically and the magnetic force were strong enough, the object could be levitated. In 1997, researchers were able to produce a magnet strong 00 enough to levitate a small frog. They reasoned that since water is a diamagnetic material, with susceptibility x -8.8 x106, and since a frog is mostly water, the frog itself would be diamagnetic. They found that the magnetic force on the frog depended on the frog's distance yabove the magnet by 00 dB 00 pH 00 where m is the frog's mass and pis the density of water (p 000 kg /ms). The permeability o free space is 4m x10 T. m A. The magnetic field B(y) above the magnet was measured to be B e with a 0.00233 m n the experiment, the frog levitated at a distance yoE 0.011 m above the magnet. What must have been the magnet's strength, Bo, in this experiment? 90 Numbe 98 If the Earth's magnetic field is typically around 45 microteslas, how many times stronger was the magnet? Number Next DIE Give Up & View Solution Previous Check Answer Copyright O 20 2016 Sapling L 37 ontact us cy policy a P g Ask me anything Available From: Not Se 4/17/2016 11:5 Due Date: Late submissions Allowed with 2 points possibl per day until 04/22/2016 11 Points Possible 15 Grade Category: Graded Description: The last three questions review tra waves from Physics 1 Policies: My Homework You can check your answers You can view solutions when you c give up on any question You have ten attempts per questio You lose 5% of the points available answer in your question for each ir attempt at that answer O eTextbook 04 PM 53% 4/17/2016

Explanation / Answer

Let mass of frog be 1 kg and force of magnet be 1 N

From given differential equation we get

F*dy=m*suceptibility*B(y)*dB(y)/density*permeability

F*y=m*susceptibility *B(y)^2/2*density*permeability

B(y)=2*F*y*density*permeability/m*susceptibility =2*1*0.011*1000*4**10^-7/(1*8.8*10^-6) =3.1416T

B(y)=B0*exp(-y^2/a)

3.1416=B0*exp(-0.011^2/0.00233

B0=3.1416/0.9494=3.309T

B0=n*Bearth

n=B0/Bearth=3.309/45*10^-6=73534.6~73535

n is number of times

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