Coulomb's law/Spring constant & Electric field problems

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A tiny sphere with a charge of +8.2 µC attached to a spring stretches 5.0 cm when influenced by two -4.0 µC spheres, leading to an initial miscalculation of the spring constant due to an incorrect distance. After correcting the distance to 0.0465 m, the spring constant was recalculated successfully. In the second problem, the electric field at point D due to two +0.95 nC charges was initially unclear, but the user eventually applied the correct approach using the equation for electric field strength. The final solution involved calculating the resultant electric field from both charges. The discussion highlights the importance of accurate distance measurements and unit conversions in solving physics problems.
Anthem26
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Homework Statement


1. A tiny sphere with a charge of q = +8.2 µC is attached to a spring. Two other tiny charged spheres, each with a charge of -4.0 µC, are placed in the positions shown in the figure, in which b = 4.2 cm. The spring stretches 5.0 cm from its previous equilibrium position toward the two spheres. Calculate the spring constant (diagram: http://imgur.com/FKcPp.gif ).

2.Two equal charges (Q = +0.95 nC) are situated at the diagonal corners A and B of a square of side x = 1.0 m as shown in the diagram. What is the magnitude of the electric field at point D (diagram: http://imgur.com/eervv.gif )?

Homework Equations


1. Coulomb's law:
F = Kq1q2/r^2

Spring Constant:
F = kx

2. Electric field:
E=kq/r2

The Attempt at a Solution


1. q1= 8.2*10^-6 q2= 4.0*10^-6 r= .027?? (I found this using Pythagorean theorem, but not sure if it's right.
So then, with that I plug it all in in coulumb's law and get 404.49N for one of the spheres and for my vertical component 404.49Nsin(65) (I got 65 from tantheta = .042/.02) = 366.59N
Because there's 2 of them I multiplied 366.59*2 = 733.18
733.19 = kx
733.19 = k(.05)
k= 14663 N/m But apparently that's not right.

2. I couldn't find a clear similar model for problem two, so this is all I have so far.
q= .95*10^-6 r= 1m
plug those variables into E=kq/r2 and I got 8540.5 N/C. I'm pretty sure there's a lot more to this, but I don't know where to go on from there.

*EDIT* ok I found what I did wrong with the first problem. I redid the whole problem and my 'r' was incorrect, it was supposed to be .0465m. After I got that, everything else was smooth sailing. Now all I need to do is learn how to do problem 2, which I have no clue. Hopefully someone could help me.
 
Last edited:
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ok I finally figured out the second question two, it took me a few attempts because I was confused with the SI units. I pretty much used this equation: sqrt (EA^2+EB^2)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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