Calculate the voltage at a point

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To calculate the electric potential at points P and M, the relevant formula is V = q/(4πεr). The discussion clarifies that the electric field (E) is not necessary for finding voltage, as voltage is a scalar quantity and does not have direction. The correct approach involves simply summing the potentials from different charges, leading to the equation V = V1 + V2. It is emphasized that direction does not matter when calculating electric potential. Understanding these concepts is crucial for solving similar problems in electrostatics.
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Homework Statement


Calculate the electric potential at (a) point P in the first figure, and (b) point M in the second.
http://www.usi.edu/science/physics/pickett/206/5p3f1.jpg

Homework Equations



V=\frac{q}{4\piεr}
E=\frac{q}{4\piεr^{2}}

The Attempt at a Solution


I'm not sure if E is really necassaryt, but I wasn't sure how else to get the direction right. So I did the vector stuff with E and got
\vec{E}=<0,\frac{-q}{2\pi\epsilon(.75)a^{2}}>

Now I'm stuck and don't know how to get to voltage
 
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You don't need the electric field - just use the definition of V.
 
Is it as easy as adding the two V's up?
Like
V_{1}+V_{2}=V
So the answer would be
V=\frac{q}{2\pi\epsilon a}

Does direction not matter?
 
Yes, you just add them up.
The potential is a scalar, not a vector, so it doesn't have a direction.
 
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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