Experimental Tasks: APhO 2022
Academic Committee: Chandan Ralekar, Siddhant Mukherjee, Siddharth Tiwary, Charudutt Kadolkar, Bipul Pal, Manoj Harbola,
Mamatha Maddur, Praveen Pathak
Acknowledgement: Chinmay Haritas, Shirish Pathare
APhO 2022
EQ1: Magnetic Black box
Based on making use of various sensors available on a smartphone.
Motivation
Hall effect based magnetic sensor to detect the magnetic field.
Experiment
Blackbox (magnet in a conducting pipe)
To identify different sections of the pipe with the help of a smartphone.
Theoretical background
The axial magnetic fieldBx of a point dipole (dipole momentM) at the distance x
Bx = µ0 2π
M x3
When the magnet is moving with a constant non-relativistic velocity
Bx(t) = µ0 2π
M (vt)3
µ0M 2πBx(t)
1/3
=vt
Three parts of the experiment:
Find the location of the magnetometer in the smartphone.
Determine the dipole momentM. Determinev of the magnet.
Simulation
1. Find the location of the magnetometer
Bw
Bl N
2. Dipole moment of the magnet
Bw = µ0 2π
M x3
2,000 4,000 6,000 8,000 0
1 2 3
·10−3
1 x3(m−3)
B(T)
data 4.00×10−7X+ 3×10−6
3. Identify sections of the pipe
When the magnet is dropped in a non magnetic conducting pipe such as aluminium or copper; m¨y =mg−ky˙
B
C D
0.6 0.7 0.8 0.9 1 1.1 4
5 6 7 8 ·10−2
t(s)
(2µ0M/4πBw)1/3(m)
AB:Aluminum
0.07 0.08 0.09 0.1 0.11
(2µ0M/4πBw)1/3(m)
BC:Wood
1 1.5 2 2.5 3 3.5 0.1
0.12 0.14 0.16
t(s)
(2µ0M/4πBw)1/3(m)
CD:Copper
Length of each section
Identify the entry and exit time stamps in the data for each section and use the obtained velocities to calculate the section lengths.
EQ2: Accoustic Black box
Doppler effect in waves and an attempt to simulate acoustically the light waves emitted from the rotating planets.
Question
y
O x
A
C B
ϕ
vs
β
D rD
θ
S
α
Sound source starts moving at A and emits frequencyf0. S is the position of the source at later time t.
You are given a detector D which you can place or move in the x−y plane.
Findf0, ω,R,vs, β, coordinates of A and C.
EQ2: Acoustic black box
Detector’s velocity: vD Vector DS: ˆ⃗ n Source’s net velocity: vT Frequency detected by the detector, when S is moving away (or
approaching) from D
f(t′) =f0c−⃗vD·ˆn(t) c ±⃗vT·ˆn(t) At large distance (or time)
vT=vs−ωR
vT=vs+ωR
vT=vs−ωR
vT=vs+ωR
S D S
Simulation
Change detector’s parameters
Asymptotic limit
Detector position rD = 10000 m, θ= 35◦
f0c (c−vs−ωR)
f0c (c+vs−ωR)
f0c (c−vs+ωR)
f0c (c+vs+ωR)
S D S
fmax+fmin
−f = c−vs ∆t = 2π 1 +vs fmax+f−fmin = c+vs
Source’s initial coordinates - Triangulation
Detector Location (rD, θ) First signal received (s)
(500,0) 1.535
(0,500) 1.273
(0,0) 1.979
Summary
How to setup an experiment.
Observational and experimental skills, visualization, data interpretation and analytical skills.