# GRIFFITH Ex 3.8 with different V

• m0nk3y
In summary, the conversation discusses the example of a grounded conducting sphere in a uniform electric field and how keeping the constant of integration in the potential equation for large r affects the electric field at large r. The question is then posed about the value of l and the change in the boundary condition. The solution involves adding V_0 to the previous answer for the potential anywhere.
m0nk3y

## Homework Statement

In the example of the grounded conducting sphere in the uniform electric field (Ex. 3.8), suppose we keep the constant of integration in V for large r, so that V -> EorPlcos$$\theta$$ + Vo the electric field at large r is unchanged. Find V outside the sphere under these conditions. What is physically different?

## The Attempt at a Solution

I think this is the same problem. I was just wondering if l = 2? And what will happened to the Vo??

Last edited:
The boundary condition is changed this will change the outcome when calculating the field outside

If I understand your question correctly, you just have to add V_0 to the previous answer for the potential anywhere.

## 1. What is the purpose of performing GRIFFITH Ex 3.8 with different V?

The purpose of performing GRIFFITH Ex 3.8 with different V is to study the behavior of materials under varying levels of applied stress and strain. This experiment helps in understanding the concept of fracture mechanics and the role of stress intensity factor in determining the strength and failure of materials.

## 2. What is the significance of using different V in GRIFFITH Ex 3.8?

The use of different V in GRIFFITH Ex 3.8 allows for a more comprehensive analysis of the fracture behavior of materials. It helps in identifying the critical stress intensity factor (Kc) at which a material will fail, and also provides information on the crack growth rate and the type of fracture that occurs.

## 3. How is GRIFFITH Ex 3.8 with different V conducted?

In GRIFFITH Ex 3.8, a material sample with a pre-existing crack is subjected to different levels of applied stress (V). The crack length is measured at each stress level, and the corresponding stress intensity factor (K) is calculated using the applied load and crack length. This process is repeated for various values of V, and the results are plotted to determine the fracture toughness of the material.

## 4. What are the limitations of GRIFFITH Ex 3.8 with different V?

One of the limitations of GRIFFITH Ex 3.8 with different V is that it assumes a linear relationship between stress intensity factor and crack length, which may not hold true for all materials. Additionally, the experiment may not accurately predict the behavior of materials under complex loading conditions or in the presence of multiple cracks.

## 5. How is GRIFFITH Ex 3.8 with different V used in real-world applications?

GRIFFITH Ex 3.8 with different V is used in various industries, such as aerospace, automotive, and construction, to determine the fracture toughness of materials. This information is crucial in designing safe and reliable structures and components. It is also used in failure analysis and quality control to detect any defects or weaknesses in materials before they are put into use.

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