Solutions A1-1 Official(English)EQ1:Official Solution1⊗A.1(1.0 pt)Move the magnet along each of the axes and notice the change in the magnetfield.For example,if the magnet is aligned along the length of the phone,and you are moving the magnet along the same direction(length of the phone),magneticfield will show the change in sign when the magnet crosses the Magnetometer.>Bw Bl Figure.11 Chandan Relekar(IISc,Bangalore),Siddhant Mukherjee(The University of Cambridge,UK),Siddharth Tiwary(IIT Powai,Mum-bai),Charudutt Kadolkar(IIT Guwahati),Praveen Pathak(HBCSE-TIFR,Mumbai),were the principal authors of this problem.The contributions of the Academic Committee and the International Board are gratefully acknowledged.give dipole moment of the magnet.A.2(2.3 pt)The set up tofind Dipole moment The magneticfield Bw of a point dipole at the distance x(x>>d)from the dipole’s center can be approximated by Rearranging above equation,we get w x3 From equation(2),a plot of B vs 1 is a straight line passing through origin.Solving the slope will the dipole moment can be calculated from the slope.A.2(cont.)Dipole moment of the Magnet:Fill the appropriate quantities.Sr.No工(cm)Bw(μT)(m__3)Bw(T)153177.6380000.00317763261841.064629.630.00184106371170.342915.450.0011703448783.691953.130.0007836959550.221371.740.00055022610403.4210000.00040342711301.21751.310.00030121812231.96578.70.00023197913181.58455.170.000181581014146.03364.430.000146031115118.72296.30.00011872121698.18244.140.000099w工3 From equation(2),a plot of B vs 1 is a straight line passing through the origin.The magnitude of B(T)A.2(cont.)data 4.00 x 10__7x+3 x 10__6 2,000 4,000 6,000 8,000 x13(m__3)Graph of Bw vs x13.10__3 3 2 1 0 Slope of the graph:4.00 x 10__7 Nm2/A Dipole moment of the magnet:2.00 Am2 B.1(0.3 pt)Rotate the smartphone and align the magnet and the pipe along the width of the phone as shown below.Consider the case when the magnet is at rest at a distance x0 from the magnetometer origin.The magnet is released along the axis of the pipe.It will start descending through the pipe.In the conducting sections of the pipe,after a brief period of accelerated motion,the magnet will attain a terminal velocity U,due to the presence of eddy current damping.In this case,the magneticfield Bw measured by the magnetometer changes with time t as Equation(3)is rearranged as B.1(cont.)Obtained profile of magneticfield vs time clearly suggests three distinct phases(AB,BC,and CD)of the magnet’s motion(see Fig.4 below).Figure(4)We collect the data of(Bw vs t)for all three phases and plot them according to Eq.(4).For the acceleration phase of the pipe(wooden section),the graph will be non-linear and for the conducting pipe sections(Al and Cu)where the magnet moves with the terminal velocities,the graph will be linear.Duration of accelerated motion before attaining terminal velocity in the conducting sections of the pipe may be neglected.It can be clearly seen from the graphs in the next sub parts that:SectionSection numberAluminium1Copper3wood2Since the copper has higher conductivity than aluminium,the terminal velocity in Cu section will be lower than Al section.B.2(2.6 pt)Terminal velocity of Magnet in aluminium section:Fill the appropriate quantities.Sr.NoBw(μT)t(s)1/3(m)U(m/s)16462.280.5340.0396026462.280.5360.03960.0135954.240.5580.04070.0644850.050.6060.04350.0654002.020.6540.04640.0663651.480.6780.04780.0672817.430.750.05220.0682397.970.7980.0550.0691911.680.870.05940.06101548.470.9420.06370.06111448.010.9660.06510.06121356.060.990.06660.06131194.261.0380.06940.06141188.091.040.06960.14151142.951.050.071 The velocity(U)column is obtained using the forward difference xn+1__xn.tn+1__tn From equation(4),a plot of vs t will be a straight line.The slope of the line will give terminal velocity.B.2(cont.)Graph of 1/3 vs t(2(t))1/3(m)2 4 0.6 0.7 0.8 0.9 1 t(s)data 0.06X+0.04.10__7 6 5 Slope of the graph:6 cm/s.Terminal velocity of the magnet in aluminium section:6 cm/s Length of the aluminium section:Slope of the graph:Not used Intercept of the graph:Not usedValues in the fourth column in the above table actually represents the distance of the magnet from the magnetometer.We calculate the velocity(column 5)of the magnet using the forward difference method.Notice that the magneticfield starts to change at 0.536 s.Hence this is the point at which the magnet starts descending.It quickly achieves the terminal velocity of 6 cm/s.A change in velocity(or departure from theflat line in U vs t curve,if you plot)occurs at 1.040 s.This suggests that the magnet moved out of the aluminium section of the pipe at this time.Length of the Al section=(1.040__0.536)x 6 cm=3.024 cm.B.3(2.2 pt)Terminal velocity of magnet in copper section:Fill the appropriate quantities.Sr.No。
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