Question

If two streams of protons move parallel to each other in the same direction, then they (a) Do not exert any force on each other (b) Repel each other (c) Attract each other (d) Get rotated to be perpendicular to each other.

Short answer

The correct answer is (b) Repel each other. This is because both streams of protons have positively charged particles, and according to Coulomb's Law, they exert a repulsive force on each other, pushing them apart.

Step-by-step solution

Understand the properties of protons

Protons are subatomic particles found in atoms and have a positive charge. In these two streams of protons, their positive charges would cause them to experience a force following Coulomb's law. This is important to determine how they would interact with one another.

Apply Coulomb's law

Coulomb's Law states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them. It can be represented mathematically as: \(F = k \frac{q1 \times q2}{r^2}\) where \(F\) is the force between the charges, \(k\) is the electrostatic constant, \(q1\) and \(q2\) are the charges of the particles, and \(r\) is the distance between them. Since both protons have a positive charge, the force expression above becomes: \(F = k \frac{( + q)( + q)}{r^2}\)

Determine the direction of the force

The force between the two streams of protons will be positive, which means that the force will be repulsive. This is due to the fact that both protons have positive charges, and like charges repel each other. Therefore, they exert a force on each other in the direction that pushes them apart.

Choose the correct answer

By understanding the properties of protons and their interaction through Coulomb's law, we can now select the correct answer: (a) Do not exert any force on each other: This is incorrect because protons have positive charges and will exert a repulsive force on each other. (b) Repel each other: This is the correct answer because like charges (both positive in this case) repel. (c) Attract each other: This is incorrect because like charges repel, not attract. (d) Get rotated to be perpendicular to each other: This is also incorrect because the force only pushes the protons apart and does not cause them to rotate. The correct answer is: (b) Repel each other.

Key concepts

Protons

Protons are one of the fundamental building blocks of matter. They are located within the nucleus of an atom and are characterized by their positive electrical charge. Each proton carries a charge of \(+1.6 \, \times \ 10^{-19} \, C\), similar in magnitude but opposite in sign to the charge of an electron.
Unlike electrons, protons are much heavier, whose mass is approximately 1,836 times that of an electron.

• Protons contribute to the identity of an element. For example, the element hydrogen has one proton, while helium has two.
• The number of protons in an atom, also known as its atomic number, determines the chemical properties of the element.

Understanding the fundamental properties of protons helps to explain their interactions with electric forces, especially when they are part of larger systems, such as parallel streams.

Electrostatic force

The electrostatic force is a type of force that acts between charged particles. It is also known as the Coulomb force, as it is the force described by Coulomb’s Law. This law provides the foundation for understanding how charged particles interact at a distance. The electrostatic force can either be attractive or repulsive, depending on the types of charges involved.
When two charged particles interact:

• Like charges, such as two positive charges or two negative charges, will repel each other.
• Opposite charges, such as a positive and a negative charge, will attract each other.

The strength of the electrostatic force between two charges can be calculated using the formula \( F = k \frac{q1 \times q2}{r^2} \). Here, \(k\) is the electrostatic constant, \(q1\) and \(q2\) are the magnitudes of the charges, and \(r\) is the distance between them.
The concept of electrostatic force is crucial to understand interactions in many physical and chemical processes, including the behavior of protons in a stream.

Charge interactions

Charge interactions underlie many phenomena in physics and chemistry, dictating how particles interact with one another. In the context of streams of protons, understanding charge interactions helps in predicting the behavior of these particles.
Charge interactions are governed by a few simple rules:

• Particles with the same type of charge will exert a repelling force on each other, while particles with opposite charges will experience an attractive force.
• The magnitude of the force is impacted by the charge sizes and the distance between them.

When dealing with streams of protons, each proton’s positive charge means that they will repel each other when placed in proximity. This repulsion affects how these streams of protons behave physically in space, pushing them apart due to their like charges.
Understanding these interactions allows us to predict the dynamics in systems that involve large numbers of charged particles, like closed circuits and particle accelerators.