3.7 Electric Forces and Free-Body Diagrams

Electric Forces and Free-Body Diagrams

Electrostatic Force & Coulomb's Law

Coulomb's Law describes the force of attraction (or repulsion) experienced between two charged point objects. Point charges simply mean that we can approximate the charges as acting from a single point. The equation for calculating electrostatic force is given below:

where q1​ and q2​ represent the two charges, r is the distance between the charges, and ϵo is the Permittivity of Free Space constant (which is given in your reference tables). Notice that if q1​ and q2​ are the same charges, we'll end up with a positive result. A positive Fe​ value leads to repulsion. 

** Physics Review Note: Electrostatic Force is a force! This means that we need to apply Newton's 3 Laws to the movement of charges too. One very common mistake is to forget that the two charged objects form a Newton's 3rd Law pair, the force between the two objects is equal in magnitude and opposite in direction.**

Electrostatic force, also known as Coulomb force, is a type of force that arises between electrically charged particles. Coulomb's law is a fundamental principle that describes the strength of the electrostatic force between two charged particles.

Here are some key points about electrostatic force and Coulomb's law:

• Electrostatic force is a fundamental force that arises between electrically charged particles. It is one of the four fundamental forces in the universe, along with the strong nuclear force, the weak nuclear force, and the gravitational force.
• Coulomb's law states that the electrostatic force between two charged particles is directly proportional to the product of the charges of the particles and inversely proportional to the square of the distance between them. This can be written as F = kq1q2/r^2, where F is the force between the particles, k is a constant known as Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between the particles.
• Coulomb's law is a fundamental principle that is used to describe the electrostatic force between charged particles in many different physical situations, including the behavior of electrons in atoms, the movement of charged particles in electric circuits, and the forces between charged particles in electrostatic discharge.
• Electrostatic force can be either attractive or repulsive, depending on the charges of the particles. If the charges are the same, the force is repulsive, while if the charges are different, the force is attractive.
• Electrostatic force is an important concept in many fields of science and engineering, including physics, chemistry, and electrical engineering. Understanding the principles of electrostatic force is essential for understanding many aspects of the natural world and for designing and building a wide range of technological devices.

Practice Questions:

1. 

Image from collegeboard.org

a) What is the direction of the force on the test charge due to the two other charges?

b) If F is the magnitude of the force on the test charge due to only one of the particles, what is the net force acting on the test charge due to both of the charges?

Answers:

a) The net force must be directed towards the bottom left corner of the page. The test charge and both Q charges are positive so they must repel. The test charge is repelled downwards and to the left.

b) The test charge experiences two forces, both of magnitude F repelling it downwards and to the left. Using the Pythagorean theorem we can determine the resulting net force

2. 

Image created by the author

Answer:

C = D > A = B > E = F

Each pair of point charges must have an equal force on them (N3L). A&B and C&D have opposite charges so therefore must attract. E&F have the same charge and must be repelling. The magnitude of the force is directly proportional to the charges and inversely proportional to the square of the separation distance, so the shorter distance in C&D results in a larger force even though the charge in B has a greater magnitude.

Free Body Diagrams (FBD)

FBDs are a very powerful tool. They are less commonly tested in this unit because they are relatively simple. Two main forces you will deal with are the Electric Force and the Gravitational Force and sometimes tension when drawing FBDs for this unit.

A common principle people forget is that if charge 1 exerts a force of X Newtons on charge 2, charge 2 also exerts a force of X Newtons on charge 1. No matter which charge is bigger they exert an equal force on each other.

We will learn about electric fields later. Knowledge of electric fields can be important in drawing FBDs because they will tell you in which direction to point the arrow for the electric force. Basically, the electric force is in the same direction as the electric field if the charged object is positive and the opposite if the charged object is negative.

The image shows arrows pointing as the Electric forces.

A free-body diagram (FBD) is a graphical representation of the forces acting on an object. It is a useful tool for understanding the physical forces at play in a given situation and for solving problems involving motion and forces. Here is a step-by-step guide for drawing a free-body diagram for a problem involving electric forces:

1. Identify the object of interest. This is the object that you will be drawing the free-body diagram for. It is important to clearly define the boundaries of the object, as this will help you to identify all of the forces acting on it.
2. Determine the direction of the forces. In a problem involving electric forces, you will need to consider both the magnitude and the direction of the forces acting on the object. The direction of the forces should be represented as arrows pointing in the direction that the force is acting.
3. Identify the electric forces acting on the object. In a problem involving electric forces, there will likely be multiple forces acting on the object. These forces may include the electric force between charged particles, the force of friction, and any other external forces such as gravity or the force of a spring.
4. Draw the free-body diagram. Using the information you have gathered, draw a diagram showing the object of interest and the direction and magnitude of all of the forces acting on it. Make sure to label each force and include a scale for the magnitude of the forces.
5. Solve the problem. Once you have drawn the free-body diagram, you can use it to solve the problem by applying the principles of Newton's laws or other relevant physical principles. This may involve calculating the acceleration of the object, the net force acting on it, or other quantities of interest.

Practice Question:

If there is an electric field towards the top of the page and there is an electron in the middle of the page, in what direction will the electric force be?

Answer:

Since an electron is negatively charged, the electric force will be opposite to the electric field. The electric force will be towards the bottom of a page.