Experiment Q1-1 Official(English)Magnetic Black box:1 Smartphones use Hall effect-based magnetometers to measure the magneticfield in its vicinity.The magnetometer measures all three components of the magneticfield.The magnetometer sensor is lo-cated on the circuit board of the phone and is not visible from outside.Magneticfield of a magnet Figure 1 shows a small bar magnet with half length d and the dipole moment M.S N 2d Figure 1 P rP Q rQ The magnitude of the magneticfield of a bar magnet in the axial direction at point P(Baxial)and at point Q on its perpendicular bisector(Bequatorial)is given by the following formulae whereμ0 is the permeability of free space(μ0/4π=10__7 NA__2),and rP,rQ are the distances between the center of the magnet to the points where thefield is measured.For the given problem,consider the magnet to be a point dipole(d<rP,rQ).Click on"EQ1-Magnetic Black Box"link in the exam portal for the experimental exam.About the simulation on the screen:You will see a canvas with a white background in the form of a grid on the screen.This grid canvas is a part of the vertical plane where the experiment is being carried out.There are four objects on the canvas:1.a smartphone 2.a magnet in blue(S)and red(N)color 3.a dark shaded hollow pipe with uniform thickness 4.a calibrated scale,which can be activated by clicking the’SHOW/HIDE SCALE’button.Intergrid spacing on the grid canvas is 1 cm.1 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.Figure 2:Screenshot of the simulation The set up:The objects can be moved by holding and dragging the mouse.Smartphone,scale,and magnet can also be rotated in the plane.The rotation control slider is available in the right panel.You can drag the slider to change the orientation.For a better control,after clicking on the slider,you can use arrow keys to rotate an object.There is a magnetometer inside the phone which measures the magneticfield of the magnet in its vicinity.The exact location of the magnetometer in the phone is not given to you.Depending on the location of the magnetometer,the right panel displays the components Bw and Bl of the magneticfield of the magnet measured by the smartphone along its width and length,respectively,as shown in Fig 2.Component Bw points to the right for the default position(portrait/vertical orientation)of the phone.Component Bl points downwards along the length of the phone.The measurement:When you click on’START MEASUREMENT’you can also see the graph of variation of Bw and Bl as a function of time.’RESET GRAPH’will erase all the values recorded in this graph.When you move the cursor over the curve in the graph obtained,you can see the value of the data point.A portion of the graph can be zoomed in by inserting the time in the"Graph start time(ti)"and the"Graph end time(tf)"fields.Smartphones may get damaged if they are exposed to high magneticfield.To prevent this,if the net magneticfield value measured by the smartphone exceeds 6500μT,the measurement will stop and you will see a warning on the right panel’Maximum Magneticfield exceeded.’Measurement is restored as soon as the magnet is moved away from the phone at a sufficient distance.Further features:The magnet can be moved by keyboard arrow keys in up-down and left-right directions.For this,click anywhere on the canvas.Afiner/coarser movement of the magnet can be achieved by clicking’2X FINER MAGNET MOVEMENT/2X COARSER MAGNET MOVEMENT’.With each clicking of these buttons,the movement will become two timesfiner/coarser.The buttons will grey-out when the maximum coarse/finer level is reached.Gravity is in the downward direction,towards the bottom of the screen.Thefloor is indicated by a red line.Consider all the objects in the plane of the screen only.More information about the pipe is given before the part(B).Consider the magnet to be held in a stationary position when you place it anywhere on the screen.Clicking on the"Drop"button will release the magnet and it will start descending.Note that the magnet can be dropped only after clicking the’START MEASUREMENT’button.The’RESET POSITION’button will bring back the magnet to the position from where it was dropped last.Objects can be moved outside the Canvas if needed.
In this experiment,consider the magnet to be a point dipole.Note that there is no error estimation required in this question.A.1 Obtain the location of the magnetometer on the phone.To help you answer this part in the answer sheet,afiner grid is made inside the schematic diagram of the phone.Intergrid spacing in thefiner grid is 2 mm.Indicate the location of the magnetometer by drawing"⊗"in the smartphone at an appropriate place.
1pt 2.3pt A.2 Plot a suitable linear graph and obtain the dipole moment of the magnet from the graph.Fill in the table for the recorded data of the method you have em-ployed.
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