LAB: LIGHT AS  A LENS TO COULOMB'S LAW EXP 32 VERNIER: SEE PAGE 154, FIG. 9.5, of  Conceptual Physics (11ed)  by Paul Hewitt or this u-tube video: http://www.youtube.com/watch?v=JW3tT0L2gpc if you do not have that book.  In the figure,  the THICKNESS OF THE LAYER OF PAINT IS like the intensity.   When you double the distance, the thickness of the layer of paint or butter thickness on the toast (see video above) goes  down by a factor of 4, not 2,  since you are squaring the denominator. The further out you go, the larger the radius r, and the smaller the intensity, just like  quiz 5 problem , #11:

http://www.nvaphysics.com/p11/au10/quizzes/QUIZ4AU10SAMPLECH9.htm

for Physics 11.

Note the formula for the surface area of a sphere is 4*pi*r2,  where r2 means the radius squared and pi = 3.14.....  The intensity = Power/(area), where Power is the energy per unit time emitted by the source and area is the surface area of the sphere: surface area = 4*pi*r2.   The  power does not depend on the radius r, only the intensity does. Thus, Power is a constant for any distance r from the source in the above formula. Power does not change as r changes.
2. If the light source is not a true  point source , then the radiation is NOT emitted with wave fronts in perfect spheres as shown in FIGURE 2 OF THE LAB HANDOUT. The picture  may not look like figure 9.5 in all directions for the same radius r and the u-tube video would not apply. Figure 9.5  and the video assume the inverse square law is true in all directions.  Now assume the  source is not a true point source, but is extended and/or may not have a spherical shape. Would light be emitted equally in all directions? Would the intensity obey the inverse square law?

ANALYSIS  QUESTIONS

1. BASED ON THE SHAPE OF THE GRAPHS, WHICH FORMULA  SHOULD YOU PICK FROM THE CHOICES GIVEN?
2.  From the curve fit menu, which  curve did you pick from the choices suggested  to you on the white board? Which function gave the best match to your curve? What was the formula  you used?  Include the actual numbers you recorded from the curve fit menu.
3.  See preliminary questions and figure 2. If the model of your experiment obeys the inverse square law,  then the concentric spherical model discussed in the preliminary questions is true.
4. Explain  experimentally why your source may not be considered a true point source as assumed in the preliminary  questions and figure 2. What were the limitations of the experimental set up that caused your results not to match the relationship predicted in the preliminary questions? List these limitations.  Think about measurement errors and reflections. What did you measure directly? What could be the cause  of reflections. Was there light from other sources in the room when you made your measurements?

Here are some suggestions: Label the charges, staring from the left, as 1, 2 and 3. 
On charge 1: Charge 2 repels it and charge 3 attracts it, so there two forces on opposite directions. 
On charge 2: Charge 1 repels it and charge 3 attracts it, so there two forces in the same direction. 
On charge 3: Charge 2 attracts it and charge 1 attracts it, so there are two forces in SAME direction, pointing left. 
Here is an example of how to do charge 1's computation.
Net force has magnitude : F_1NET   =  k|q₁q₃|/(0.70)²   -   k|q₁q₂|/(0.35)²  .  If this difference is negative,  the force points left. Otherwise, it points  right. 
Try the same subtraction method with charge 2. Be careful;  the distances used in the formulae are equal. 
For charge 3, the computation is similar to charge 1  but the force points  left; get the magnitude by adding  force magnitudes due to  charge 1 and 2.

14. Please email  with comments on this exercise. What gave you trouble?
I can say this: Each of the 4 forces points away from the center along a diagonal. 

Let us label the charges counterclockwise starting  from the charge in the upper right corner, which we will call  charge q₁.  Without loss of generality, let us find the net force on that charge using the component method .  
F_1NETx  =  F₁₂  + F₁₃cos45.   
F_1NETy  =  F₁₃sin45 +  F₁₄. 

 
F₁₂ =   k|q₁q₂|/a²   .
F₁₃ =   k|q₁q₃|/(2a²).
F₁₄ =   k|q₁q₄|/a² .

Note: a = 0.100 m and 6x10^-3 C =  q₁   = q₂  =  q₃ = q₄  .

For charge 2:

F_2NETx  =  - F₂₁  -  F₂₄cos45.  
F_2NETy =  F₂₄sin45 +  F₂₃.

F₂₁ =   k|q₂q₁|/a²   .
F₂₄ =   k|q₂q₄|/(2a²).
F₂₃ =   k|q₂q₃|/a² .

Same procedure for charge 3 and charge 4.