Notes, summaries, assignments, exams, and problems for Physics

Coulomb's Law: The magnitude of each of the electrical forces that interact with two point charges at rest is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them. Coulomb's law is valid only in stationary conditions, ie when there is movement of charge or, as an approximation when the movement takes place at low speeds and in uniform rectilinear trajectories. That is why it is called electrostatic force.

The magnitude of this force is worth: F = K • Qq / r ²

The value of CTE of proportionality K depends on the chosen system of units and the medium interposed between the load. It is, tannate, a universal constant. If the charges are in vacuum and... Continue reading "Fundamental Concepts of Electrostatics: Coulomb's Law" »

Fundamental Concepts and Assumptions

Temperature is a physical quantity whose value is an index of the degree of molecular kinetic energy.

Temperature Scales

Temperature scales are based on two fixed points:

• The conventional temperature scale.
• The absolute temperature scale (Kelvin, °K).

First Postulate: Temperature and Thermal Gradient

Temperature is a scalar quantity that, at each point, is a function of its position coordinates and time.

Defining the Thermal Gradient

If we consider a stationary field, we can define the gradient of $T$ at each point as a vector given by the expression:

This vector gives us the thermal gradient at each point of the field.

Statement of the First Postulate

The First Postulate states: "Heat is a form of energy exchange

Wave Reflection Study

Purpose

To study the reflection of a plane wave, generated by a wave source, off different obstacles.

Planning

1. Position the right triangle reflector in the form of a right angle.
2. Generate plane waves incident upon the reflector.
3. Affix paper to the table. Use a ruler to draw one or more lines to show the front of the incident wave and the reflected wave front. Ensure the ruler is parallel to the corresponding disturbance.
4. Trace the position of the reflective barrier.
5. Repeat steps for two other positions of the triangle.

Part 2: Reflection in a Curved Obstacle

1. Trace the circular barrier on a new sheet of paper.
2. Mark the position where the reflected waves converge.
3. Turn off the generator. Use your fingertip to produce a circular pulse

Key Kinematics Concepts

Reference System

A reference system is a coordinate system (O, X, Y) combined with a clock, used to define the position and motion of objects.

Position

Position is the location of a body in space, defined by coordinates within a chosen reference system.

Trajectory

The trajectory is the imaginary path or line described by a moving body, formed by the sequence of positions it occupies over time.

Distance Traveled (Path Length)

Distance traveled (or path length) is the total length of the path covered by a body along its trajectory.

Displacement

Displacement is the vector difference between a body's final and initial positions, indicating the change in position and direction. It is measured in meters (m).

Velocity

Velocity is a vector... Continue reading "Fundamental Concepts of Motion in Physics" »

Photomultiplier Characteristics

What is dark current?

The dark current is a small amount of current flowing in the photomultiplier even when it is not illuminated. This current should be minimized for accurate measurements. The region between 800 V and 1300 V is often ideal for operating the photomultiplier.

The primary source of dark current is the thermionic emission rate from the photocathode and dynodes. Other sources include:

• Leakage current
• Incandescent lighting phenomena
• Field emission
• Current from residual gas ionization
• Radioactive contamination within the device materials

What is the photomultiplier gain?

The gain (G) of a photomultiplier is the ratio between the number of electrons at the output and the number of photons incident on the photocathode.... Continue reading "Photomultiplier Dark Current, Gain & Lifetime Measurements" »

Concept of Slope and Gradient

The closeness of curves indicates a steep slope, while a large separation indicates a slight incline. This equidistance, whenever we have to compare the two cases, is the same. The equidistance of curves in a plane is unique.

• A series of concentric curves, where the heights rise to the center, indicates a rise or hill.
• A series of concentric curves, in which the dimensions decrease toward the center, indicates a depression or hollow.

We define slope as the ratio between the horizontal and vertical displacement, always looking from the top down. The gradient is defined as the ratio between the vertical and horizontal displacement.

Alignment

• Natural Distance (Dn): Dn is the distance traveled on the ground, following the

**Fe, Co, Ni: Ferromagnetic Materials**

_Iron (Fe), Cobalt (Co), and Nickel (Ni)_ are ferromagnetic materials. They strongly attract metals and exert attractive or repulsive forces on other materials.

**Early Discoveries in Magnetism**

• **William Gilbert:** Identified North and South Poles as magnetic.
• **First Discovered Natural Magnet:** Magnetite (iron oxide (Fe₃O₄)) and Magnesia (Chinese).

**Electric and Magnetic Fields**

• **Charge (Q) at rest:** Creates an electric field.
• **Moving charge:** Creates an electromagnetic field.

Analogy:

• Computer storage ↔ Electric field
• Mass ↔ Gravitational field
• Magnet ↔ Magnetic field

**Key Figures in Electromagnetism**

• **1831 Michael Faraday:**

  Introduced the concept of lines of force to explain the behavior of forces

Motor Performance Problem

A motor has a resistance of 250 Ω and operates at 100 V at 25 °C. The temperature coefficient of resistance (α) at 25 °C is 0.0018 /°C. We need to determine the following:

Questions for Analysis

1. The resistance value when the temperature is 50 °C.
2. The current absorbed from the network when the temperature is 25 °C and 50 °C.
3. The cost of the energy consumed in 120 minutes at 50 °C if the cost per kWh is $1.
4. At what temperature and why does the motor consume less energy?

Principles of Electromagnetism

Induced Electromotive Force (EMF)

When a conductor of length (l) moves with a constant velocity (v) within a magnetic field of induction (B), an electromotive force (EMF) is induced across its ends.

• Perpendicular Motion:

Vacuum and Pressure Measurement Devices

Cold Cathode Ionization Transducer

The cold cathode transducer is based on the principle of measuring the ion current produced by a high-voltage discharge. Electrons detached from the cathode take a spiraling motion as they move through a magnetic field on their way to the anode. This spiraling motion ensures that the mean free path of the electrons is greater than the distance between the electrodes.

This extended path increases the possibility of collisions with residual gas molecules, leading to increased ion current. Consequently, the cathode discharge is maintained at a lower pressure, indicating a higher vacuum level. While this instrument cannot degas as quickly as a hot filament gauge, it is significantly... Continue reading "Vacuum Transducers and Pressure Control Mechanisms" »