Sample Lab Report For Phy10004.pdf

Laboratory  report  –  example  report  for  PHY10004  students,  taken  from  Lab  1   This  is  not  a  “perfect”  report,  but  it  includes  most  of  the  important  features.    

PHY10004  Lab  report  for  Experiment  4  –  Coulomb’s  Law  

  Aim:  This  experiment  was  an  investigation  of  the  force  between  two  charged   objects.  It  examined  the  relationship  between  the  electric  force  and  the   separation  of  the  charges,  and  compared  it  to  the  expectation  of  Coulomb’s  Law.     Theory   Electric  charge  comes  in  two  types,  described  by  the  signs  positive  and  negative,   and  objects  with  a  net  charge  exert  a  force  on  each  other.  If  two  objects  have  the   same  sign  of  charge,  then  they  repel  each  other,  and  if  they  have  opposite  signs  of   charge  they  attract  each  other.   Keep  the  theory   section  as   relevant  to  the   experiment  as   possible   (especially   concepts  that   will  be  used  in   analysis).  

The  magnitude  of  the  force  between  point  charges  depends  on  the  size  of   each  charge  (q1  and  q2)  and  the  distance  they  are  separated  (r).  This  is   mathematically  described  by  Coulomb’s  Law:     𝑘𝑞! 𝑞! 𝐹= 𝐹 =   𝑟! where  k  is  the  Coulomb  constant,  in  SI  units  k  =  9  ×  109  Nm2/C2.   This  is  an  example  of  an  inverse-­‐square  law,  which  occurs  in  many   interactions  in  physics  (e.g.  the  gravitational  force).   If  the  relationship  between  quantities  is  expected  to  be  a  power  law,  then  a   useful  way  to  analyse  experimental  data  is  to  use  properties  of  logarithms,  as   shown:   if    𝑍 = 𝑋𝑌 !  then  log 𝑍 = log 𝑋 + 𝑁log 𝑌  

 

so  plotting  log(Z)  vs  log(Y),  keeping  X  constant,  would  produce  a  linear  graph   with  gradient  N.   Method   The  main  apparatus  used  consisted  of  two  identical  spheres,  about  30  mm  in   diameter,  coated  with  a  conductive  material.  One  of  the  spheres  is  attached  to  a   torsion  balance,  and  the  other  is  on  a  sliding  mount  that  can  be  moved  closer  or   further  away.  The  general  set-­‐up  is  shown  in  the  diagram  below:     moveable   mount  

 

torsion   adjustment  

spheres  

 

  distance   scale  

   

torsion   balance  

  The  general  procedure  was  as  follows;   • •

move  the  spheres  to  maximum  separation   use  the  high-­‐voltage  probe  to  charge  each  sphere  using  6.0  kV  

Diagrams  are   almost  always   useful  in  the   method.  They  can   be  hand-­‐drawn,   computer-­‐drawn,  or   even  a  photograph   (but  it  must  be   clearly  labeled)  

• • • • •

switch  the  high-­‐voltage  source  off  immediately  after  charging   carefully  slide  the  moveable  sphere  mount  to  the  desired  separation   turn  the  torsion  adjustment  knob  to  return  the  torsion  balance  to   equilibrium  (i.e.  the  two  marks  on  the  balance  are  aligned)   write  down  the  the  separation  distance  and  the  angle  of  the  torsion   knob   repeat  for  the  next  separation  distance  

Using  point-­‐ for  to   describe  steps   is  fine,  but   avoid  simply   copying  the   instructions   from  the  lab   notes.  

The  angle  of  the  thread  in  the  torsion  balance  is  directly  proportional  to  the  force   it  applies  to  the  sphere,  and  therefore  it  is  proportional  to  the  electric  force  felt   by  the  sphere.     There  is  no   need  to   Results   reproduce  the   The  data  collected  is  shown  in  the  table  on  the  attached  worksheet.   information   Uncertainties  are  relatively  small,  and  can  be  approximated  as  +/-­‐  0.5  degrees   from  the  lab   worksheet,  but   for  angle  and  +/-­‐  0.5  cm  for  separation  distance.   Two  graphs  were  drawn,  also  on  the  attached  worksheet.  The  graph  of   separation  vs  angle  clearly  shows  a  non-­‐linear  relationship,  but  the  graph  of   log(distance)  vs  log(angle)  seems  quite  linear,  and  a  line  of  best  fit  has  been   drawn.   Analysis   The  slope  of  the  log(distance)  vs  log(angle)  graph  should  reveal  the   relationship  between  the  electric  force  and  separation.  Here  is  the  calculation   of  the  slope:  

you  should   clarify  any   important   details.  In  some   cases  you  may   want  to   construct   additional   graphs.  

two  well-­‐separated  points  on  the  line  of  best  fit  are  (2.48,  3.00)  and  (2.90,  2.025)   this  gives  a  gradient  of  !.!"#!!.!! = −2.3.   !.!"!!.!" An  estimate  of  the  uncertainty  in  the  gradient  is  given  by  the  steepest  and  least-­‐ steep  lines  that  reasonably  fit  the  data,  as  shown  by  the  dotted  lines  on  the   graph.  The  difference  in  the  gradients  of  these  lines  is  0.26,  giving  an   uncertainty  in  the  gradient  of  +/-­‐  0.13.   This  result  gives  the  relationship  between  force  and  separation  as  𝐹 ∝ 𝑑 ! ,  with   an  experimental  value  of  n  =  –2.3  +/-­‐  0.13,  which  is  about  a  5%  uncertainty.  

The   calculation  of   the  extreme   lines  of  best   fit  should   have  been   shown  here.  

The  expectation  from  Coulomb’s  Law  is  n  =  –2,  that  is,  an  inverse  square  law.   This  experimental  result  is  not  in  agreement  with  Coulomb’s  Law,  giving  a  value   of  n  that  is  15%  too  large.  Our  results  indicate  that  the  electric  force  between  the   charges  decreases  faster  than  expected  by  Coulomb’s  Law.  Some  possible   explanations  for  this  include  the  slow  discharge  of  the  spheres,  the  finite  size  of   the  spheres,  and  unaccounted  external  forces.  These  possibilities  are  discussed   in  the  next  paragraph.   The  spheres  will  gradually  lose  their  charge  through  interaction  with  the   surrounding  air.  It  is  possible  that  the  timing  of  the  experiment  was  not   controlled  properly,  and  that  there  was  less  charge  on  the  spheres  when  the   larger  distances  were  investigated.  The  spheres  are  not  well  modeled  by  point   charges,  and  it  may  be  that  the  finite  size  of  the  spheres  causes  a  small   deviation  from  an  exact  inverse  square  law.  Finally,  there  are  many  external   forces  that  are  difficult  to  control  completely,  such  as  air  currents  or  charge   interactions  with  the  experimenters’  hands.  These  might  alter  the  size  of  the  

It  is   important  to   give  as  m uch   detail  as   possible  when   discussing   potential   sources  of   uncertainty.  

force  measured  by  the  torsion  balance.  Another  thing  to  consider  is  the  small   number  of  data  points  that  have  been  used  for  the  analysis.  Four  points  is   probably  too  few,  and  the  range  of  the  data  is  also  small  (i.e.  the  range  of   distances  does  not  ever  cover  a  factor  of  2  in  separation  change).   Conclusion   This  experiment  was  able  to  investigate  the  nature  of  the  electric  force  between   two  charged  objects.  By  using  two  identical  spheres,  with  identical  charges  on   them,  the  only  quantity  that  should  have  affected  the  size  of  the  force  was  the   distance  between  the  two  charges,  which  was  varied  in  a  controlled  manner.  The   electric  force  was  not  measured  directly,  but  a  torsion  thread  was  used  to  apply  a   force  that  balanced  the  electric  force,  and  the  angle  of  torsion  thread  could  be   carefully  controlled.  Although  no  exact  measurements  were  made  of  the   important  physical  quantities  (i.e.  the  size  of  the  force,  the  amount  of  charge  on   the  spheres),  the  mathematical  relationship  between  force  and  separation  was   able  to  be  determined.   Our  results  showed  a  clear  non-­‐linear  relationship  between  force  and  separation,   as  expected  from  the  inverse  square  law  in  Coulomb’s  Law.  However,  when  a  log-­‐ log  plot  was  analysed,  the  results  showed  a  deviation  from  an  exact  inverse   square  law.  The  data  gave  force  proportional  to  dn,  with  n  =  –2.3  +/-­‐0.13.  Whilst   this  is  close  to  agreement  with  Coulomb’s  Law,  a  larger  data  set  would  be  useful   to  reduce  the  uncertainty.  There  are  also  several  factors,  such  as  air  currents  and   external  forces,  that  could  be  better  controlled  to  improve  the  experiment.      

 

The   conclusion   should   provide  the   reader  with  a   concise   summary,   and  relate   the  original   aim  and   method  to  the   results  and   discussion.  

Lab 1 –

WORKSHEET

PHY10004

  LAST  NAME:  T ry-Hard   STUDENT  ID:  5 55128x   • •

FIRST  NAME:  A nonym ous   TABLE  #:  5  

DAY: Friday  

Experiment  4  –  Coulomb’s  Law     (a)  Charge  the  two  spheres  with  the  same  voltage,  and  measure  the  force   between  them  as  a  function  of  separation.  Torsion  angle  is  directly  proportional   to  force.   Separation, d [cm]

Log(d)

12

Torsion angle, θ [degrees] 19

2.48

2.94

14

14

2.64

2.64

16

10

2.77

2.30

18

8

2.89

2.08

 

θ˚ 20  

TIME: 2:30  

Log(θ)   3.0  

x  

Log(θ)

x  

2.8  

x  

x  

2.6  

x  

10  

2.4  

x  

x  

2.2  

x   0  

2.0   10  

12  

14  

16  

18  

d  (cm)  

2.40  

2.50  

2.60  

2.70  

2.80  

2.90   Log(d)  

      Make  sure  everything  is   completed  on  the  worksheet  –   leave  no  unexplained  gaps.   Importantly,  graphs  should   have  axes  that  are  clearly   labeled,  with  units  indicated   and  appropriate  choice  of  scale   to  use  as  much  of  the  available   space  as  possible.