Physics 2 Final Exam Review
The Organic Chemistry Tutor・40 minutes read
A dust particle has a net charge of -5.6 micro coulombs due to an imbalance of protons and electrons, while various calculations demonstrate the forces and electric fields generated by point charges, such as a 0.281 newton force on a negative charge near a positive one. Additionally, the transformations in potential energy and electric potential are illustrated through examples, showing how charges interact and the work done in moving them within electric fields.
Insights
- A dust particle contains a significant imbalance of charge, with 5 x 10^13 protons and 8.5 x 10^13 electrons, leading to a net negative charge of -5.6 micro coulombs, illustrating the fundamental principles of charge balance and its implications in physical systems.
- The calculation of electric forces and fields is grounded in established formulas, such as F = k * (q1 * q2) / r² and E = k * q / r², which allow for precise determination of the forces acting on charges in various configurations, highlighting the predictable nature of electric interactions.
- The arrangement and potential differences between charged plates can be systematically analyzed to yield electric field strengths, as seen with a voltage difference of 120 volts across 10 centimeters resulting in an electric field of 1200 volts per meter, demonstrating the relationship between voltage, distance, and electric field strength in practical applications.
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Recent questions
What is electric charge?
Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It exists in two types: positive and negative. Protons carry a positive charge, while electrons carry a negative charge. The interaction between these charges is governed by Coulomb's law, which states that like charges repel each other, while opposite charges attract. The unit of electric charge is the coulomb (C), and it can be quantified in terms of the number of elementary charges, where one elementary charge is approximately 1.6 x 10^-19 coulombs. Understanding electric charge is essential in fields such as physics and engineering, as it plays a crucial role in electricity, magnetism, and the behavior of atoms.
How to calculate electric force?
To calculate the electric force between two point charges, you can use Coulomb's law, which is expressed by the formula F = k * (q1 * q2) / r². In this equation, F represents the electric force, k is Coulomb's constant (approximately 9 x 10^9 N·m²/C²), q1 and q2 are the magnitudes of the two charges, and r is the distance between the centers of the two charges. The force is attractive if the charges are of opposite signs and repulsive if they are of the same sign. This formula allows you to determine the strength and direction of the force acting between the charges, which is fundamental in understanding electric interactions in various physical systems.
What is an electric field?
An electric field is a region around a charged object where other charged objects experience a force. It is a vector field, meaning it has both magnitude and direction, and is represented by the symbol E. The strength of the electric field created by a point charge can be calculated using the formula E = k * q / r², where k is Coulomb's constant, q is the charge creating the field, and r is the distance from the charge. The direction of the electric field is defined as the direction a positive test charge would move if placed in the field. Electric fields are crucial in understanding how charges interact with each other and are fundamental in the study of electromagnetism.
What is electric potential energy?
Electric potential energy is the energy that a charged object possesses due to its position in an electric field. It is defined as the work done to move a charge from a reference point (usually at infinity) to a specific point in the field without any acceleration. The formula for calculating electric potential energy (U) is U = q * V, where q is the charge and V is the electric potential at the location of the charge. This energy can be positive or negative depending on the nature of the charge and the electric field. Understanding electric potential energy is essential in fields such as physics and electrical engineering, as it helps explain how energy is stored and transferred in electric systems.
How to find voltage between two points?
To find the voltage (electric potential difference) between two points in an electric field, you can use the formula V = W/q, where V is the voltage, W is the work done to move a charge between the two points, and q is the magnitude of the charge. Alternatively, if you know the electric field (E) and the distance (d) between the two points, you can calculate voltage using the formula V = E * d, where the direction of the electric field is taken into account. Voltage is a measure of the potential energy per unit charge and is crucial for understanding how electric circuits operate, as it drives the flow of current through conductors.
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Summary
00:00
Electric Charge and Force Calculations Explained
- A dust particle has 5 x 10^13 protons and 8.5 x 10^13 electrons, resulting in a net charge of -5.6 x 10^-6 coulombs or -5.6 micro coulombs.
- To find the net charge, subtract the number of protons from electrons: 5 x 10^13 - 8.5 x 10^13 = -3.5 x 10^13, then multiply by the charge of a proton (1.6 x 10^-19 coulombs).
- A negative 40 micro coulomb charge is 8 meters east of a 50 micro coulomb charge; the net electric force on the negative charge is 0.281 newtons directed west.
- Use the formula F = k * (q1 * q2) / r^2, where k = 9 x 10^9 N·m²/C², q1 = 50 x 10^-6 C, q2 = 40 x 10^-6 C, and r = 8 m.
- The electric field created by a negative 75 micro coulomb charge at 50 cm (0.5 m) east is approximately 2.7 x 10^6 N/C directed west.
- Calculate the electric field using E = k * q / r^2, substituting k = 9 x 10^9 N·m²/C², q = 75 x 10^-6 C, and r = 0.5 m.
- A negative 80 micro coulomb charge in a 4 x 10^5 N/C electric field experiences a force of 32 newtons directed south.
- The electric force is calculated as F = E * q, where E = 4 x 10^5 N/C and q = 80 x 10^-6 C.
- The change in potential energy of an electron accelerated through a 700-volt potential difference is -1.12 x 10^-16 joules.
- Use the formula ΔPE = q * ΔV, where q = -1.6 x 10^-19 C and ΔV = 700 V, resulting in a negative change in potential energy.
21:37
Calculating Electric Fields and Potentials Explained
- Position the negative plate at the bottom and the positive plate at the top, connecting them to a battery; the long side indicates the positive terminal, and the short side indicates the negative terminal.
- Assign plate A a potential of 0 volts and plate B a potential of 120 volts, ensuring the voltage difference is 120 volts, with B always 120 volts higher than A.
- The separation distance between the plates is 10 centimeters, which converts to 0.1 meters by dividing by 100, necessary for calculating the electric field strength.
- Calculate the electric field strength using the formula: electric field = voltage / distance; thus, 120 volts / 0.1 meters equals 1200 volts per meter.
- The voltage increases by 120 volts every 0.1 meters, resulting in a potential gradient of 12 volts per centimeter, allowing for voltage calculations at various distances from plate A.
- For a positive charge of 70 nano coulombs at a distance of 5 meters, use the formula for electric potential: V = kq/r, where k = 9 x 10^9, yielding an electric potential of 126 volts.
- For three point charges of 50 micro coulombs each, calculate the total electric potential at point P by summing individual potentials: V1 = kq1/r1, V2 = kq2/r2, V3 = kq3/r3.
- The distances for the charges are 4 meters for q1, 5 meters for q2, and 3 meters for q3, leading to a total electric potential of -172,500 volts due to the proximity of negative charges.
- To calculate work required to move two 50 micro coulomb charges from 500 meters to 1 meter apart, use the formula: W = -k * q1 * q2 * (1/rb - 1/ra).
- The final work calculated is -22.455 joules, indicating that moving like charges closer increases potential energy, resulting in negative work done.
43:14
Net Electric Force on Charge in Square
- Four point charges, each with a magnitude of 200 microcoulombs, are arranged in a square with a side length of 3 meters.
- The net electric force on charge q4 is calculated by considering the forces exerted by charges q1, q2, and q3.
- The force on q4 due to q1 (F41) is calculated using the formula F = k * (q1 * q4) / r², resulting in a magnitude of 40 newtons directed east (0 degrees).
- The force on q4 due to q3 (F43) is also 40 newtons, but directed south (270 degrees), calculated similarly with the same distance of 3 meters.
- The force on q4 due to q2 (F42) is calculated using the distance of √18 meters, resulting in a magnitude of 20 newtons directed southwest (225 degrees).
- The x-components of the forces are calculated: F41x = 40 cos(0) = 40, F43x = 40 cos(270) = 0, and F42x = 20 cos(225) = -14.14, summing to 25.86 newtons.
- The y-components are calculated: F41y = 40 sin(0) = 0, F43y = 40 sin(270) = -40, and F42y = 20 sin(225) = -14.14, summing to -54.14 newtons.
- The magnitude of the net force on q4 is calculated as √(25.86² + (-54.14)²), resulting in 60 newtons.
- The direction of the net force is determined using the arctangent of the y-component over the x-component, yielding a reference angle of 64.47 degrees, adjusted to 295.53 degrees in quadrant four.
- The electric force between two point charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance, with a new force calculated as 9600 newtons when charge magnitudes and distance are adjusted.
