# How to Calculate Potential and Speed of a Proton Near a Barium Nucleus?

• XxXDanTheManXxX
In summary, a barium nucleus with a charge of +56e has a potential of V = 0 at a radius of 10-12 m. If a proton is released from this point, it will move at a speed determined by the equation \nabla \vec{E} = \frac{\rho}{\epsilon_0}. It is recommended to become familiar with gaussian pill box and its applications for future studies in E&M.
XxXDanTheManXxX
A barium nucleus has a charge of q = +56e (where e is the proton charge).
a. find the potential V at a radius of 10-12 m from the Nucleus. If a Proton is released from this point, how fast will it be moving when it is 1 m from the nucleus? Note: Assume V (infinity=0)
Any help?

I suggested in some of you other threads gaussian pill box. Learn to use it and love it. As an undergrad it looks like you have 1 or two more semsters of E&M and it won't go away. It might chagne a little though
$$\nabla \vec{E} = \frac{\rho}{\epsilon_0}$$

Sure, I can help with this problem. To find the potential V at a radius of 10^-12 m from the nucleus, we can use the formula V = kq/r, where k is the Coulomb's constant (9x10^9 Nm^2/C^2), q is the charge of the nucleus (+56e), and r is the distance from the nucleus (10^-12 m). Plugging in these values, we get V = (9x10^9)(56e)/(10^-12) = 5.04x10^20 V.

To find the speed of a proton when it is 1 m from the nucleus, we can use the conservation of energy principle. At a distance of 10^-12 m, the proton has a potential energy of qV = (1.6x10^-19 C)(5.04x10^20 V) = 8.064x10^2 J. At a distance of 1 m, the potential energy will be converted into kinetic energy, so we can set the two equal to each other: qV = (1/2)mv^2, where m is the mass of the proton (1.67x10^-27 kg) and v is the speed we are looking for. Solving for v, we get v = √(2qV/m) = √(2(8.064x10^2 J)/(1.67x10^-27 kg)) = 1.6x10^9 m/s.

I hope this helps! Let me know if you have any other questions.

## What are electric charges?

Electric charges are physical properties of matter that cause it to experience a force when placed in an electric field. There are two types of electric charges: positive and negative. Like charges repel each other, while opposite charges attract each other.

## How do electric charges affect each other?

Electric charges interact with each other through the electromagnetic force. Like charges repel each other because they have the same type of charge, while opposite charges attract each other because they have different types of charge. The strength of the force between two charges depends on the magnitude of the charges and the distance between them.

## What is the study of electric charges called?

The study of electric charges is called electrostatics. It is a branch of physics that deals with the behavior of electric charges at rest. This includes topics such as electric fields, electric potential, and capacitance.

## How is the study of electric charges relevant in everyday life?

Understanding electric charges is essential in many aspects of daily life. For example, it is the basis for how electricity works, which is crucial for powering homes and devices. It also plays a role in the functioning of electronics, such as computers and smartphones. Additionally, electric charges are involved in chemical reactions, which are essential for many processes in the human body.

## What are some common applications of the study of electric charges?

Some common applications of the study of electric charges include the development of new technologies, such as batteries and electric motors. It is also used in the fields of telecommunications, medicine, and environmental science. Understanding electric charges is also crucial in the design and operation of power grids and electrical systems.

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