# Electrodynamics in FE Electrical Exam

Understanding the principles of electrodynamics in the FE Electrical exam is a vital exam aspect according to NCEES® FE Electrical exam guidelines. Electrodynamics deals with uncovering the complex depths of electric and magnetic fields.

FE exam aspirants embarking on the FE Electrical Exam journey will find that mastering electrodynamics is not just an academic requirement but a gateway to resolving the real-world problems associated with electrical systems and electromagnetic fields.

This detailed Electrodynamics study guide for the FE Electrical Exam study guide involves all the Electrodynamics study resources for FE Electrical exam preparation and promising success in the career afterward.

If you are looking forward to practicing Electrodynamics formulas and answering electrodynamics practice questions for the FE Electrical Exam, study this detailed guide until the end.

## Electric Charges and Fields

Charge (q) is a fundamental property of matter. It is quantized, meaning it occurs in discrete units. The charge can be defined as

q=n⋅e, where

• n is an integer representing the number of elementary charges (electrons or protons).
• e is the charge of an electron

Coulomb’s Law gives the electrostatic force between two point charges:

F = (k * q1 * q2) / r^2

Where:

• F: Electrostatic force between the charges.
• k: Coulomb’s constant ≈ 8.99 x 10^9 Nm^2/C^2.
• q1, q2: Magnitudes of the charges.
• r: Distance between the charges.
• ε: Permittivity of the medium. ε ≈ 8.85 x 10^-12 C^2/(Nm^2) for vacuum or air.

Coulomb’s Law describes the electrostatic force between charges, similar to Newton’s Law of Gravitation, which describes the gravitational force between masses. The similarity lies in their mathematical form, both involving an inverse-square relationship. However, there are key differences:

• Nature of Force – Coulomb’s Law describes electric forces between charges, which can be attractive or repulsive depending on the charges’ signs. On the other hand, Newton’s Law of Gravitation only describes attractive gravitational forces between masses.
• Strength of Force – The electrostatic force between charges is much stronger than the gravitational force between masses. This is due to the significant difference in the strengths of the forces of nature.

### Electrostatic Force and Its Nature

The electrostatic force’s nature depends on the charges’ nature. Charges of the same sign (positive or negative) repel each other, while charges of the opposite sign attract each other. This contrasts the gravitational force, where all masses attract each other.

Electric field lines visualize the electric field around charges. They depict the direction and strength of the electric field. The electric field at a point is the force experienced by a positive test charge (​qo) placed at that point, divided by the magnitude of the test charge.

Electric field lines originate from positive charges and terminate on negative charges. The closer the lines are to each other, the stronger the electric field in that region.

#### Point Charge (q) vs.Test Charge (qo​)

• q represents an actual charge that generates an electric field.
• qo is a hypothetical small positive test charge used to measure the electric field at a point. It’s considered small enough not to affect the field itself significantly.

### Electric Field and Electric Field Intensity

#### Electric Field

An electric field is a region where an electric charge experiences a force.

It is the force experienced per unit positive charge placed at a given point in space.

E = F/q

#### Electric Field Intensity

The Electric Field Intensity (E) at a point is the force experienced by a test charge (q0) placed at that point.

The formula for electric field intensity due to a point charge (Q) is given by:

E = (k * Q) / r^2

For positive charges:

• E points radially outward from the charge (away from it).

For negative charges:

• E points radially inward toward the charge (toward it).

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## Electric Potential and Capacitance

Electric potential, often called voltage, is a fundamental concept in electrostatics that describes the potential energy per unit charge at a point in an electric field.

It’s a scalar quantity measured in volts (V). Electric potential is related to the electric field (E) at a point in space by the equation:

V=-E.r

Where:

• The dot (.) signifies the dot product between electric intensity (E) and displacement of charge (r).
• The negative sign indicates that electric potential decreases in the direction of the electric field.

### Electric Potential as Potential Difference or Voltage

The voltage between two points in an electric field is also called the potential difference (V). It’s the work to move a unit of positive charge from one point to another against the electric field. Mathematically:

Vdiff=VB-VA

### Voltage as Work Done per Unit Charge

Voltage (V) or electric potential difference is also defined as the measure of the energy required to move a unit positive charge (q) from one point to another against the electric field.

Mathematically, it can be expressed as:

V = W/q

Knowing all these Electrodynamics formulas for the FE Electrical Exam is recommended to solve problems with different data and values.

### Providing Energy from a Voltage Source (AC or DC)

When we talk about providing energy from an AC (alternating current) or battery source to a circuit, we are essentially referring to creating a potential difference (voltage) between two points in the circuit.

In the case of an AC source, the voltage alternates in direction periodically, while in the case of a battery, it remains relatively constant.

#### AC Source

In an AC circuit, the voltage changes direction periodically, causing charges to oscillate back and forth. This oscillation of charges is what enables the flow of electric current.

The AC source provides the energy required to push charges from a region of lower electric potential to a higher electric potential and vice versa. The charges continually gain and lose energy as they move in response to the changing potential difference.

#### Battery Source

In a battery-powered circuit, the battery establishes a constant potential difference between its terminals. The positive terminal has a higher electric potential, and the negative terminal has a lower electric potential.

This potential difference serves as the driving force for charges to move through the circuit. When a circuit is closed, charges flow from the negative terminal to the positive terminal, releasing energy.

Imagine a circuit with a battery connected to a light bulb. The battery provides a potential difference (voltage) between its terminals. When the circuit is closed (completed), charges start moving through the circuit.

As they pass through the light bulb’s filament, they encounter resistance, which requires work to overcome. This work is provided by the energy stored in the battery.

The battery’s voltage represents the energy per unit charge that the battery can provide. It’s similar to the concept of lifting an object against gravity. You need to provide energy to lift the thing to a certain height.

Similarly, in an electric circuit, the voltage (potential difference) provides the energy needed to move charges from a lower potential to a higher potential, just as lifting an object requires energy to move it to a higher altitude.

### Understanding Electromagnetic Fields in Fe Electrical Exam With Analogies

The concept of electric potential and potential difference has analogies with other forms of potential energy:

Gravitational Potential Energy – In a gravitational field, objects at higher altitudes have higher gravitational potential energy. Moving an object upwards requires adding energy, while it naturally moves downwards due to the force of gravity. Similarly, in an electric field, charges moving from a lower to a higher electric potential require external energy while naturally moving in the opposite direction.

Thermal Potential Energy – Temperature differences between two points drive heat flow. Heat naturally flows from high-temperature to low-temperature areas, and work is needed to reverse this process. This parallels the movement of charges from high to low electric potential, where charges move spontaneously and require energy against the potential difference.

#### Example From Daily Life

• Waterfall Analogy – Imagine a waterfall. Water at the top has high gravitational potential energy, losing potential energy as it falls to a lower height. Similarly, charges at higher electric potential have higher electric potential energy, and they lose energy as they move to points of lower potential.
• Thermal Analogy – Consider a hot object and a cold object. Heat naturally flows from the hot object to the cold one. To reverse this process, work needs to be done. Similarly, positive charges move from high electric potential to low potential (like heat flowing from hot to cold), and work is needed to move them against the electric field.

### Electric Potential Due to Point Charges and Continuous Charge Distributions

The electric potential (V) at a point in space due to a point charge (q) is given by:

Whereas, continuous charge distributions, like a uniformly charged ring, disk, or line, you integrate over the charge distribution to find the electric potential (dV) contributed by a tiny element of charge (dq) at a distance r from the point of interest. Then integrate all such elements to get the total potential.

dV= K.dq/r

For a 1D continuous charge distribution, like a charged line, integrate along the line:

V= K.dx/r

For a 2D distribution, like a charged disk, integrate over the disk’s area:

V= K.dA/r

For a 3D distribution, like a charged solid sphere, integrate over the volume:

V= K.dV/r

### Energy Stored in Capacitors

The energy (U) stored in a capacitor with capacitance (C) with charge stored (Q) and voltage (V) across its terminals is given by: U=1/2 QV or 1/2 CV2 or Q2/2C

Knowing how to derive this Electrodynamics formula for FE Electrical Exam can be insightful. Let’s see the origin of the formula for energy stored in a capacitor.

We know that the work done in moving a charge dq across a potential difference V is given by dW=V⋅dq. In the case of a capacitor, as it charges up, the voltage across it increases.

Consider a capacitor with charge Q and voltage V across its plates. Let’s start with the definition of capacitance C, which relates to charge and voltage: Q=C⋅V.

Now, let’s consider an incremental change in charge dQ and the corresponding change in voltage dV. The work done in moving this incremental charge dV. The work done in moving this incremental charge dQ against the changing voltage dV is:

dW=V⋅dQ

Substitute the relation Q=C⋅V:

dW=(C⋅V)⋅dV

Now, we can integrate both sides to find the total work done W in charging the capacitor from an uncharged state (initially Q=0 and V=0) to its charged state (final Q and V):

W=0vC.Vdv

W=C0vVdv

W=1/2 C V2 dv

So the energy stored will be:

U=1/2 C V2 dv

## Electromagnetic Waves – A Spectrum of Radiant Energy

Electromagnetic waves are a fundamental aspect of electromagnetic theory, showcasing the intricate interplay between electric and magnetic fields. They propagate through a vacuum or various media, carrying energy and information across vast distances.

These waves are characterized by their wavelength (λ) and frequency (f), connected by the speed of light (c) in a vacuum as c = λf.

### The Electromagnetic Spectrum

The electromagnetic spectrum encompasses a diverse range of waves, each with distinct properties and applications:

Radio waves possess the longest wavelengths, ranging from about 1 millimeter to 100 kilometers, with frequencies from 3 kHz to 300 GHz. They are used for telecommunications, broadcasting, and radar systems. Examples include AM and FM radio frequencies.

#### Microwaves

Microwaves have shorter wavelengths, ranging from 1 millimeter to 1 meter, with frequencies from 300 MHz to 300 GHz. They find utility in microwave ovens, satellite communication, and radar technology. WiFi and Bluetooth also operate in this range.

Infrared radiation lies just beyond the visible spectrum. It spans wavelengths from about 700 nanometers to 1 millimeter, with frequencies from 300 GHz to 430 THz. Infrared is utilized in thermal imaging, remote controls, and various industrial applications for non-contact temperature measurement.

#### Visible Light

Visible light is the narrow band of electromagnetic waves that human eyes can perceive. It consists of colors ranging from violet (shortest wavelength of about 380 nanometers) to red (longest wavelength of about 750 nanometers).

Ultraviolet (UV) waves possess shorter wavelengths than visible light, spanning 10 nanometers to 400 nanometers, with frequencies from 750 THz to 30 PHz. They are commonly associated with tanning beds, sterilization, and UV spectroscopy.

#### X-rays

X-rays are highly energetic waves used extensively in medical imaging (X-ray radiography and CT scans) due to their ability to penetrate tissues. They have wavelengths ranging from about 0.01 to 10 nanometers, ranging from 30 PHz to 30 EHz.

#### Gamma Rays

Gamma rays have the shortest wavelengths and the highest energy in the spectrum. They have wavelengths less than 0.01 nanometers and frequencies exceeding 30 EHz. They are utilized in various fields, including cancer treatment and nuclear research.

## Transmission Lines – Uncovering Insights into Electromagnetic Signals

Transmission lines are foundational components in electrical engineering, enabling the efficient transfer of electromagnetic signals over distances. Understanding their behavior involves the manipulation of electric and magnetic flux.

### Electric Flux and Transmission Lines

Electric flux, quantified by Gauss’s law, measures the flow of an electric field through a closed surface. In transmission lines, this principle is vital for analyzing electric potential distribution along the line and ensuring minimal signal loss.

### Magnetic Flux and Transmission Lines

Magnetic flux, encapsulated by Ampere’s law and Faraday’s law, pertains to the magnetic field passing through a given area. In transmission lines, these laws guide the assessment of magnetic interference and inductance, both critical for signal integrity and design considerations.

### Importance of Electrodynamics in FE Electrical Exam involving Transmission Lines

Electrodynamics in power systems for the FE Electrical Exam involves studying Transmission and distribution lines behavior which is profoundly influenced by electrodynamics. The interdependence of electric and magnetic fields necessitates a comprehensive grasp of electromagnetic theory.

Engineers must consider wave propagation, impedance matching, reflection, and attenuation while designing and optimizing transmission lines for applications like power distribution, telecommunications, and high-speed data transmission.

## Applications of Electrodynamics

Electrodynamics might seem complex, but it’s the invisible force behind many electrical technologies we use daily. Let’s explore how these principles come alive in three critical electrical engineering applications:

### Voltage Transformers

These devices ensure our homes and businesses receive electricity at the correct voltage. The magic behind them lies in electromagnetic induction. When a changing magnetic field interacts with a coil of wire, it induces a voltage. Transformers utilize this principle to step up (increase) or step down (decrease) voltage levels in AC power systems. Understanding electrodynamics empowers you to analyze how transformers operate and calculate their efficiency, ensuring proper power delivery.

### Electric Motors

Electric motors are ubiquitous, powering household appliances and driving industrial machinery. Their core functionality is rooted in electromagnetism. Motors convert electrical energy into mechanical motion by applying magnetic forces to a current-carrying conductor (rotor) using stationary electromagnets (stator). Knowledge of electrodynamics equips you to understand how motors operate, the control mechanisms that govern their speed and direction, and even troubleshoot potential problems that might arise.

### Transmission Lines

Delivering electrical power over long distances efficiently requires careful consideration of electrodynamics principles. Factors like line impedance (resistance to current flow) and power factor (ratio of real power delivered to apparent power) play a crucial role. Understanding these electrodynamic concepts is essential for designing and analyzing transmission lines, ensuring minimal power losses during transmission.

Electrodynamics plays a fundamental role in the electrical technologies we rely on daily, from powering our homes to driving industry. Understanding these core principles gives us a deeper appreciation for the invisible forces that keep our world running.

### Conclusion

You now have a clear understanding of Electrodynamics in the FE Electrical Exam. Electrodynamics applications in the FE Electrical Exam go beyond just pen and paper. It has vast implications for your professional life ahead.

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Understanding electromagnetic fields in FE Electrical Exam is also important to get a more detailed insight into the interplay of electric and magnetic fields. It is recommended to read our detailed guide to electromagnetism.

Licensed Professional Engineer in Texas (PE), Florida (PE) and Ontario (P. Eng) with consulting experience in design, commissioning and plant engineering for clients in Energy, Mining and Infrastructure.