Average electric field over a spherical surface

In summary, the formula for calculating average electric field over a spherical surface is E = Q/4πε<sub>0</sub>R<sup>2</sup>, where E is the average electric field, Q is the total charge enclosed by the surface, ε<sub>0</sub> is the permittivity of free space, and R is the radius of the spherical surface. The average electric field over a spherical surface is the average of all the electric field values at different points on the surface, whereas the electric field at a specific point on the surface is the electric field value at that particular point. Yes, the average electric field over a spherical surface can be negative if the enclosed charge is negative or if the enclosed
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alexmahone
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Homework Statement
Show that the average electric field over a spherical surface, due to charges outside the sphere, is the same as the field at the center.
Relevant Equations
This is where I'm stuck.
I'm sure the average is going to be an integral, but [itex]\displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a}[/itex] gives me a scalar, not a vector.
 
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Related to Average electric field over a spherical surface

1. What is the definition of average electric field over a spherical surface?

The average electric field over a spherical surface is the average strength of the electric field at all points on the surface. It takes into account both the magnitude and direction of the electric field at each point.

2. How is the average electric field over a spherical surface calculated?

The average electric field over a spherical surface is calculated by taking the integral of the electric field over the surface and dividing it by the surface area. This can be represented by the equation Eavg = 1/4πε0 * ∫E * dA, where ε0 is the permittivity of free space, E is the electric field, and dA is the differential surface area.

3. What is the significance of the average electric field over a spherical surface?

The average electric field over a spherical surface is significant because it helps us understand the overall behavior of the electric field in a given region. It can also be used to calculate the total electric flux through the surface, which is an important concept in the study of electromagnetism.

4. How does the average electric field over a spherical surface relate to the electric field at a single point?

The average electric field over a spherical surface takes into account the electric field at all points on the surface, while the electric field at a single point only represents the strength and direction of the electric field at that specific point. However, the average electric field can be used to calculate the electric field at a single point by taking the limit as the surface area approaches zero.

5. Can the average electric field over a spherical surface be negative?

Yes, the average electric field over a spherical surface can be negative. This indicates that the electric field is pointing in the opposite direction of the surface normal at some points on the surface. However, the magnitude of the average electric field will always be positive.

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