Solved: Griffiths Problem 3.1: Calculating Average Potential on Sphere

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In summary, to calculate the average potential on a sphere, you will need to use the formula V_avg = (1/4πε)(Q/R), where V_avg is the average potential, ε is the permittivity of free space, Q is the total charge on the sphere, and R is the radius of the sphere. This formula is specifically for a sphere and cannot be used for other shapes. Calculating average potential on a sphere has significance in understanding electric fields and has practical applications. The units used for the variables in the formula may vary, but typically V_avg is measured in volts, ε in farads per meter, Q in coulombs, and R in meters.
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[SOLVED] Griffiths Problem 3.1

Homework Statement


This question refers to Griffith's E and M textbook.

I am stuck trying to calculate the average potential on the sphere due to the enclosed charge. It seems like he used something like Gauss's Law but I don't see how to get the average potential from Gauss's Law.


Homework Equations





The Attempt at a Solution

 
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The integral G does on the preceding page is the same integral as for the average V on the sphere for a point charge within the sphere.
 

1. How do I calculate the average potential on a sphere?

To calculate the average potential on a sphere, you will need to use the formula V_avg = (1/4πε)(Q/R), where V_avg is the average potential, ε is the permittivity of free space, Q is the total charge on the sphere, and R is the radius of the sphere.

2. What is the formula for solving Griffiths Problem 3.1?

The formula for solving Griffiths Problem 3.1 is V_avg = (1/4πε)(Q/R), where V_avg is the average potential, ε is the permittivity of free space, Q is the total charge on the sphere, and R is the radius of the sphere.

3. Can I use this formula for any shape other than a sphere?

No, this formula is specifically for calculating the average potential on a sphere. For other shapes, different formulas will need to be used.

4. What is the significance of calculating average potential on a sphere?

Calculating average potential on a sphere can help us understand the behavior of electric fields and how they interact with charges on a spherical surface. It is also used in many real-life applications, such as in designing electrical systems and devices.

5. What units should I use for the variables in the formula?

The units used for the variables in the formula may vary depending on the system of units being used. However, typically, the units for the average potential (V_avg) are volts (V), the units for the permittivity of free space (ε) are farads per meter (F/m), the units for the charge (Q) are coulombs (C), and the units for the radius (R) are meters (m).

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