A Charge Of $7.2 \times 10^{-5} , C$ Is Placed In An Electric Field With A Strength Of 4.8 × 10 5 N C 4.8 \times 10^5 \, \frac{N}{C} 4.8 × 1 0 5 C N ​ $. If The Electric Potential Energy Of The Charge Is 75 J, What Is The Distance Between The Charge And The

$$

=====================================================

Introduction

Electric potential energy is a fundamental concept in physics that describes the energy stored in a system due to the interaction between charged particles and an electric field. In this article, we will explore the relationship between electric potential energy, electric field strength, and the distance between a charged particle and the electric field. We will use the given values of electric potential energy, electric field strength, and charge to calculate the distance between the charge and the electric field.

Electric Potential Energy

Electric potential energy is defined as the energy required to move a charged particle from one point to another in an electric field. It is a measure of the work done against the electric field to move the charge. The electric potential energy of a charge in an electric field is given by the equation:

$$U = qV$$

where $U$ is the electric potential energy, $q$ is the charge, and $V$ is the electric potential.

Electric Field Strength

Electric field strength is a measure of the force exerted on a charged particle by an electric field. It is defined as the force per unit charge and is measured in units of $\frac{N}{C}$. The electric field strength is given by the equation:

$$E = \frac{F}{q}$$

where $E$ is the electric field strength, $F$ is the force, and $q$ is the charge.

Calculating the Distance

To calculate the distance between the charge and the electric field, we can use the equation:

$$U = qEV$$

where $U$ is the electric potential energy, $q$ is the charge, $E$ is the electric field strength, and $V$ is the distance between the charge and the electric field.

Rearranging the equation to solve for $V$, we get:

$$V = \frac{U}{qE}$$

Substituting the given values, we get:

$$V = \frac{75 \, J}{(7.2 \times 10^{-5} \, C)(4.8 \times 10^5 \, \frac{N}{C})}$$

Calculating the Distance

To calculate the distance, we need to perform the calculation:

$$V = \frac{75 \, J}{(7.2 \times 10^{-5} \, C)(4.8 \times 10^5 \, \frac{N}{C})}$$

$$V = \frac{75 \, J}{3.456 \times 10^1 \, J/m}$$

$$V = 21.67 \, m$$

Conclusion

In this article, we have explored the relationship between electric potential energy, electric field strength, and the distance between a charged particle and the electric field. We have used the given values of electric potential energy, electric field strength, and charge to calculate the distance between the charge and the electric field. The calculated distance is 21.67 m.

Discussion

The calculation of the distance between the charge and the electric field is an important concept in physics. It has many practical applications in fields such as engineering, materials science, and biophysics. The understanding of electric potential energy and electric field strength is crucial in designing and developing new technologies.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
• [3] Tipler, P. A. (2012). Physics for Scientists and Engineers. W.H. Freeman and Company.

Further Reading

• [1] Electric Potential Energy: A Comprehensive Review
• [2] Electric Field Strength: A Guide to Understanding
• [3] Calculating Distance in Electric Fields: A Step-by-Step Guide
  

$$

=====================================================

Introduction

Electric potential energy is a fundamental concept in physics that describes the energy stored in a system due to the interaction between charged particles and an electric field. In this article, we have explored the relationship between electric potential energy, electric field strength, and the distance between a charged particle and the electric field.

Q&A

Q: What is electric potential energy?

A: Electric potential energy is the energy required to move a charged particle from one point to another in an electric field. It is a measure of the work done against the electric field to move the charge.

Q: What is electric field strength?

A: Electric field strength is a measure of the force exerted on a charged particle by an electric field. It is defined as the force per unit charge and is measured in units of $\frac{N}{C}$.

Q: How is electric potential energy related to electric field strength and distance?

A: Electric potential energy is related to electric field strength and distance by the equation:

$$U = qEV$$

where $U$ is the electric potential energy, $q$ is the charge, $E$ is the electric field strength, and $V$ is the distance between the charge and the electric field.

Q: How do you calculate the distance between a charge and an electric field?

A: To calculate the distance, you can use the equation:

$$V = \frac{U}{qE}$$

Substitute the given values of electric potential energy, charge, and electric field strength into the equation to solve for the distance.

Q: What is the distance between the charge and the electric field in this problem?

A: The distance between the charge and the electric field is 21.67 m.

Q: What are some practical applications of electric potential energy and electric field strength?

A: Electric potential energy and electric field strength have many practical applications in fields such as engineering, materials science, and biophysics. They are crucial in designing and developing new technologies.

Q: What are some common mistakes to avoid when calculating electric potential energy and electric field strength?

A: Some common mistakes to avoid when calculating electric potential energy and electric field strength include:

• Failing to convert units correctly
• Forgetting to include the charge in the calculation
• Not considering the direction of the electric field

Conclusion

In this article, we have explored the relationship between electric potential energy, electric field strength, and the distance between a charged particle and the electric field. We have also answered some common questions about electric potential energy and electric field strength.

Discussion

The calculation of electric potential energy and electric field strength is an important concept in physics. It has many practical applications in fields such as engineering, materials science, and biophysics. The understanding of electric potential energy and electric field strength is crucial in designing and developing new technologies.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
• [3] Tipler, P. A. (2012). Physics for Scientists and Engineers. W.H. Freeman and Company.

Further Reading

• [1] Electric Potential Energy: A Comprehensive Review
• [2] Electric Field Strength: A Guide to Understanding
• [3] Calculating Distance in Electric Fields: A Step-by-Step Guide