Electric Potential & Sphere

[erinec]

Homework Statement

http://img156.imageshack.us/img156/2111/picture2ox5.png

Homework Equations

N/A

The Attempt at a Solution

The correct answer is supposed to be: V1 > V2 > V3 > V4 = V5 = V6

But it is kind of weird...

since charge only accumulates at the surface, you would think that V1=V4=V5=V6=0.

My question is: Why is V1 randomly higher?...

 

[snapback]

hi erinec,

it is the resultant electric field which is zero in a sphere (due to charge accumulation on the surface) but a zero fiel means a constant potential (and not zero potential) , that's why V4=V5=V6

the capacitance of a charged sphere is C=4*pi*eps0*R, this means smaller C for the smaller sphere. Now it is Q=C*V -> V=Q/C -> the surface of the smaller sphere has a higher potential V (for a charge coming from infinity) than the surface of the larger sphere. Inside of the smaller sphere, the potential is again constant. This gives V1>V4=V5=V6

 

[nlightner]

I can provide a possible explanation for why V1 is higher than V2, V3, V4, V5, and V6 in this scenario. It is important to understand that electric potential is a measure of the potential energy per unit charge at a certain point in an electric field. In this case, we have a spherical object with a positive charge at its center. This creates an electric field that radiates outward from the center, with the electric potential decreasing as you move away from the center.

Now, let's consider the points V1, V2, V3, V4, V5, and V6. V1 is located at the center of the sphere, where the electric field is strongest due to the high concentration of positive charge. Therefore, the electric potential at V1 will be the highest compared to the other points.

As you move outwards from the center, the electric field decreases and the electric potential decreases accordingly. However, at points V4, V5, and V6, the electric potential remains the same because these points are located on the surface of the sphere, where the charge is distributed evenly. This means that the electric field is also evenly distributed, resulting in the same electric potential at all points on the surface.

In conclusion, V1 is higher than the other points because it is at the center of the sphere, where the electric field is strongest. The other points have lower electric potentials because they are further away from the center and the electric field decreases with distance.