The activation energy of the reaction was determined to be 259 kJ/mol using the Arrhenius equation.
Given data: Rate constant at 298 K = 3.61 × 10⁻¹⁵ s⁻¹ Rate constant at 425 K = 8.66 × 10⁻⁷ s⁻¹.
The activation energy of the reaction is calculated using Arrhenius equation.
Arrhenius equation is given as \(k = Ae^(-Ea/RT)\)Where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant.
The activation energy can be determined as follows:
Taking the ratio of the two rate constants:
\(k1/k2 = (Ae^(-Ea/RT₁))/(Ae^(-Ea/RT₂))k1/k2 = e^(Ea/R(1/T₂ - 1/T₁))\),
\(8.66 × 10⁻⁷ s⁻¹ / 3.61 × 10⁻¹⁵ s⁻¹ = e^(Ea/R(1/425 - 1/298))2.4 × 10⁸ = e^(Ea/8.314(0.001956))\)
ln\(2.4 × 10⁸ = (Ea/8.314)(0.001956)Ea = 2.59 × 10⁵ J/molEa = 259 kJ/mol\)(Approximately).
Therefore, the activation energy of the reaction is 259 kJ/mol.
Activation energy (Ea) is the minimum energy required for a chemical reaction to occur.
The rate constant of a reaction depends on the activation energy of the reaction, the temperature, and the pre-exponential factor.
The Arrhenius equation can be used to calculate the activation energy of a reaction.
The first-order rearrangement of ch3nc is measured to have a rate constant of 3.61 × 10⁻¹⁵ s⁻¹ at 298 K and a rate constant of 8.66 × 10⁻⁷ s⁻¹ at 425 K.
Using the Arrhenius equation, the activation energy of the reaction was determined to be 259 kJ/mol.
The activation energy of the reaction was determined to be 259 kJ/mol using the Arrhenius equation.
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during an extreme emergency, your body must make sure it is in the correct mode to save your life. what modes?
During an extreme emergency, our body must be in fight or flight mode. There are three stages of stress response during an emergency. They are alarm, resistance, and fatigue.
Alarm is the first stage among the 3 stages in the stress response system. In alarm stage, the body and mind go on high alert. It is sometimes called the "fight or flight response". It prepares the body to either go for defending itself or to flee from a threat.
When you perceive a situation or event to be a threat, your body begins a stress response. The nervous system and the endocrine system are active during the body's response to stressors. This response is involuntary or automatic and happen in three stages.
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For a constant applied force, how does increasing the mass of an object affect it acceleration?
Express the answer in scientific notation:
5.0 x 10^-7mg + 4 x 10^-8mg
Answer:
4 * 10^-8 mg = .4 * 10^-7 mg divide and multiply by 10
5.0 x 10^-7mg + .4 x 10^-7 mg = 5.4 x 10^-7 mg
Also 5.4 x 10^-7 mg = 5.4E-7 mg
The right of the trustor to pay off all the debt and stop the foreclosure proceedings after the auction sale is called A) equitable redemption. B) deed in lieu of foreclosure. C) redemption by action. D) statutory redemption.
The right of the trustor to pay off all the debt and stop the foreclosure proceedings after the auction sale is called statutory redemption.
This right is available in some states and allows the trustor to reclaim their property by paying the full amount of the outstanding debt plus any additional fees within a specified period of time after the foreclosure sale. Equitable redemption is the right of the trustor to pay off the debt and stop the foreclosure proceedings before the sale. Deed in lieu of foreclosure is an agreement between the trustor and the lender to transfer the property to the lender in exchange for the cancellation of the debt. Redemption by action is a legal action that allows the trustor to redeem the property by paying the full amount of the outstanding debt after the foreclosure sale.
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True or False. The speed of light is sped up by dense media.
Light from a 560 nm monochromatic source is incident upon the surface of fused quartz (n=1. 56) at an angle of 60°. what is the angle of reflection from the surface?
The angle of reflection is "60°".
Here we apply the law of the concept of reflection then we get the final answer easily.
The angle of incident = angle of reflection
Then, the Angle of the incident =60°
What is reflection?
Reflection is the phenomenon of light rays returning to the source after striking an obstruction. It resembles the way a ball bounces when we toss it on a hard surface. Some of the light rays that strike an item are reflected, some of them travel through it, and the remainder are absorbed by the object.The given values are:Light from a monochromatic source,= 560 nmThe angle of incidence,= 60°The surface of fused quartz (n),= 1.56When a light ray does exist on a flat surface, the law or idea of reflection should apply since it includes both the reflected and "normal" light rays at the mirror surface.According to the above law,Angle of incident = angle of reflectionThen, Angle of incident =60°.To learn more about reflection visit: https://brainly.com/question/15487308
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A man lifts a bucket of water from a well that is 7 meters deep. The bucket and water together weigh 50 Newtons. He turns the crank handle with a force of 5 Newtons. The effort force is blank. (Fill in the blank)
A) 70 meters
B) 5 N
C) 50 N
D) 25 N
Answer:
Work = Work out
Work in = 5 N * d where d is the distance the handle travels
Work out = 50 N * 7 m = 350 Joules
d = 50 N * 7m / 5 N = 70 m
This is the distance traveled by the force of 5 N
A man lifts a bucket of water from a well that is 7 meters deep. The bucket and water together weigh 50 Newtons. He turns the crank handle with a force of 5 Newtons. The effort force is 70 Newtons.
What is Effort force?If a force is applied for a machine to move or change the position of the object is known as Effort force.
The effort force formula can be described as,
Fe = Fl. dl / de
Fe is effort force (N, lb)
Fl is load force (N, lb) (note that weight is a force)
dl is distance from load force to fulcrum (m, ft)
de is distance from effort force to fulcrum (m, ft)
Here, the given data to find the effort force is,
Fl =50 Newtons
dl = 7 meters
de = 5 Newtons.
Substituting all the values, we get,
Fe = 350/5
Fe = 70 Newtons.
Thus, the effort force is 70 Newtons.
Hence, Option A is the correct answer.
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Why does a balloon when robbed on a wall sticks to the wall
Answer:
static electricity
Explanation:
An air-track glider of mass 0.25 kg moving at 0.60 m/s collides with and sticks to a glider of mass 0.50 kg at rest. How much kinetic energy is converted into other forms of energy as a direct result of this collision?
Answer:
0.03 Joules have been converted into other forms of energy as the direct result of the collision.
Explanation:
Let's start studying the conservation of momentum for the system:
\(P_i=P_f\\(0.25\,kg)\,{0.6\,m/s)+(0.5\,kg)\,(0\,m/s)=(0.25\,kg+0.5\,kg)\, v_f \\\\\\ 0.15\,kg\,m/s=0.75\,kg\,\,v_f\\v_f=0.15/0.75\,\,m/s\\v_f=0.2\,\,m/s\)
Now that we know the speed of the newly created object, we can calculate how the final kinetic energy differs from the initial one:
\(K_i=\frac{1}{2} (0.25)\,(0.6)^2+\frac{1}{2} (0.5)\,(0)^2=0.045\,\,J\\ \\K_f=\frac{1}{2} (0.75)\,(0.2)^2=0.015\,\,J\\\)
Then, when we subtract one from the other, we can estimate how much kinetic energy has been converted into other forms of energy in the collision:
0.045 J - 0.015 J = 0.03 J
Which term best describes the phrase "something that happens"?
A. Experiment
B. Observation
C. Hypothesis
D. Phenomenon
The phenomenon is the term that best describes the phrase "something that happens", therefore the correct answer is option D.
What is science?The deliberate, scientifically justified quest and utilization of knowledge and comprehending of the natural and improvements in living standards are what is known as science.
As given in the problem,
Which term best describes the phrase "something that happens"?
A. Experiment
B. Observation
C. Hypothesis
D. Phenomenon
The phenomenon is the term used to define the process of happening things that may be natural or anthropologic.
Thus, The phrase "something that happens" is best described by the word "phenomenon," hence option D is the appropriate response.
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Help with 7 - 9 please!
Answer:
Try lookin those questions up on Brainly
Explanation:
You are in an elevator that is accelerating you upward at 4.55 m/s^2. How much time does it take you to reach a speed of 11.0 m/s?
Answer:
t = 2.01 seconds
Explanation:
It is given that,
The acceleration of the elevator is 4.55 m/s².
We need to find time taken by you to reach a speed of 11 m/s
The initial velocity of the person is equal to 0 (at rest). Let t is the time.
Using equation of kinematics as follows :
v = u +at
Acceleration = g-a and u = 0
So,
\(t=\dfrac{v}{g-a}\\\\t=\dfrac{11}{10-4.55}\\\\t=2.01\ s\)
So, 2.01 seconds is taken to reach a speed of 11 m/s.
Due to our ozone layer, ultraviolet astronomy must be done from space, true or false?
True, due to the protective nature of the ozone layer and the absorption of UV radiation, conducting ultraviolet astronomy from space is necessary to gather accurate and detailed data about celestial objects and phenomena emitting UV light.
The ozone layer plays a crucial role in protecting the Earth's surface from harmful ultraviolet (UV) radiation. It absorbs a significant portion of the Sun's UV rays, preventing them from reaching the surface and potentially causing damage to living organisms.
As a result, to observe and study ultraviolet astronomy, which involves the detection and analysis of celestial objects and phenomena emitting UV radiation, observations must be conducted from space. By observing from space, astronomers can bypass the Earth's atmosphere, including the ozone layer, and directly capture the UV light from celestial sources.
UV astronomy satellites and telescopes, such as the Hubble Space Telescope and the International Ultraviolet Explorer (IUE), have been specifically designed and deployed to conduct observations in the ultraviolet spectrum. These instruments are situated above the Earth's atmosphere, enabling them to capture and analyze UV radiation without interference from atmospheric absorption.
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The diagram below shows a light ray striking a plane mirror surface at an angle of 40° to the normal.
Which of the following diagrams shows the ray that is reflected from the plane mirror surface?
Answer:
we need to see all of the options
Explanation:
Explain relation between work and energy
Answer:
Work is directly proportional to energy.
Explanation:
Work is said to be done when a body is displaced from one position to another. A force is required to make this displacement. This force applied is a kind of energy that is kinetic in nature. So when we displace an object by applying force, we are changing its kinetic energy to do the work.
This clarifies the relation between work and energy as :-Work Done = Change in Kinetic Energy.
A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. How deep is the water?
A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. 21 meters deep is the water.
The time it takes for the sound wave to travel from the boat to the bottom of the lake and back is given by:
t = 2d/v
Where:
d = depth of the water
v = speed of sound in water (1,500 m/s)
We can solve for d by rearranging the equation as:
d = v × t/2
Where:
t = the time it takes for the sound wave to travel from the boat to the bottom of the lake and back, which is equal to twice the time it takes for the sound wave to travel from the boat to the bottom of the lake.
The time it takes for the sound wave to travel from the boat to the bottom of the lake is given by:
t = d/v
Where:
d = distance traveled by the sound wave (which is equal to the depth of the water)
v = speed of sound in water (1,500 m/s)
We can substitute this expression for t into the equation for d to get:
d = v × d/2v
Simplifying this expression, we get:
d/0.007 = 2 × 1500
d = 21 meters
Therefore, the depth of the water is approximately 21 meters.
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The Equilibrium Rule states that the vector sum of all forces acting on an object with zero acceleration is equal to zero, this is definition of?
The Equilibrium Rule is a fundamental principle in physics that states that the vector sum of all the forces acting on an object with zero acceleration is equal to zero.
In simpler terms, if an object is at rest or moving at a constant velocity, the net force acting on it must be zero. This principle can be applied to various situations, including stationary objects, objects in motion, and even systems with multiple objects.
For example, if a book is placed on a table and remains stationary, the forces acting on it must balance out to zero. This means that the force of gravity acting downward must be equal to the force of the table pushing upwards.
Understanding and applying the Equilibrium Rule is essential in many fields, including engineering and mechanics, and is a foundational concept for further study in physics.
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The Equilibrium Rule is a fundamental principle in physics which states that if an object has zero acceleration, then the vector sum of all forces acting upon it must also be equal to zero. This means that the forces acting in opposite directions must be equal in magnitude and opposite in direction, creating a state of balance or equilibrium.
The Equilibrium Rule can be expressed mathematically as:
ΣF = 0
where ΣF represents the vector sum of all forces acting on the object.
When an object is at rest or moving with constant velocity, its acceleration is zero. According to Newton's Second Law, the net force acting on an object is equal to the product of its mass and acceleration:
ΣF = ma
If the acceleration is zero, then the net force must also be zero. This means that the vector sum of all forces acting on the object must be zero, as stated by the Equilibrium Rule.
It is important to note that the Equilibrium Rule only applies to objects with zero acceleration, and that objects in motion may have a non-zero net force acting on them, which causes them to accelerate.
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how to find velocity with force and mass ?
Answer:
Explanation:
F=ma
a=change in velocity/time
f=m*change in velocity/time
velocity= Force*time/mass
The energy used to move against the magnetic force is stored as (pick one: potential or kinetic)
Which statement about the diagram is accurate?
The forces pointing right and left are balanced.
The forces pointing up and down are balanced.
The forces pointing up and down are unbalanced.
There is a net force of 200 N to the left.
Answer:
The answer is B The forces pointing up and down are balanced
Explanation:
Know the different types of energy
Answer:
Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms
Nuclear Power Nuclear power is a clean and efficient way of boiling water to make steam, which turns turbines to produce electricity. Nuclear power plants use low-enriched uranium fuel to produce electricity through a process called fission
Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects
Electricity is the flow of electrical power or charge. It is a secondary energy source which means that we get it from the conversion of other sources of energy,
Mechanical Energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces
Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid
Light commonly refers to electromagnetic radiation that can be detected by the human eye.
Motion in physics, change with time of the position or orientation of a body. Motion along a line or a curve is called translation
Electromagnetic radiation in classical physics, the flow of energy at the universal speed of light through free space or through a material medium in the form of the electric and magnetic fields that make up electromagnetic waves such as radio waves, visible light, and gamma rays
Heat is the form of energy that is transferred between systems or objects with different temperatures
Which statement about force is incorrect
A. Some forces cause objects around us to move.
B. Some forces keep objects around us from moving
C. Force is the ability to change motion and transfer matter.
D. Force causes changes in the motion and energy of matter.
Answer:
I don't know sorry brother/sister
Explanation:
please mark as brilliant
The half-life of iodine-131 is 8.07 days. If 0.25 g are left after 40.35 days, how many gramswere in the original sample?
Given data
*The half-life of iodine-131 is t = 8.07 days
*The amount of quantity left is N = 0.25 g
*The number of days is T = 40.35 days
The expression for the radioactivity decay is given as
\(N=N_0(\frac{1}{2})^{\frac{T}{t}}\)Substitute the values in the above expression as
\(\begin{gathered} \text{0}.25=N_0(\frac{1}{2})^{\frac{40.35}{8.07}} \\ N_0=8\text{ g} \end{gathered}\)Answer:
See below
Explanation:
40.35 days / (8.07 day per half life) = 5 half lives
.25 = x ( 1/2)^5
.25 / ( 1/2)^5 = x = 8 gm originally
mine C contient 1000 mg
d'acide ascorbique. Il
se prend dans un verre
d'eau de 20 CL.
1. Une orange contient
115 mg d'acide ascorbique. Combien faut-il d'oranges
pour obtenir la même masse d'acide ascorbique que
le comprimé ?
2. Il faut environ trois oranges pour obtenir 200 mL de
jus. Quelle est la concentration en acide ascorbique
du jus d'orange ?
3. Quel volume de la solution obtenue avec le comprimé
dans le verre contient la même masse d'acide ascor-
bique que ces trois oranges ?
4. Quel volume d'eau faut-il ajouter au verre contenant
le comprimé pour obtenir la même concentration en
acide ascorbique que le jus d'orange ?
Answer:
Explanation: honestly i don’t speak spanish so please explain with english
The maximum allowable potential difference across a 250 mH inductor is 360 V . You need to raise the current through the inductor from 1.5 A to 2.5 A . What is the minimum time you should allow for changing the current?
This question involves the concepts of potential difference, inductance, and current.
The minimum time that should be allowed for the current to change is "0.694 ms".
The inductance of an inductor is given by the following formula:
\(E=L\frac{\Delta I}{\Delta t}\\\)
where,
E = potential difference across the inductor = 360 volts
L = inductance of the inductor = 250 mH = 0.25 H
ΔI = change in current = 2.5 A - 1.5 A = 1 A
Δt = time required = ?
Therefore,
\(\Delta t = \frac{(0.25\ H)(1\ A)}{360\ volts}\)
Δt = 6.94 x 10⁻⁴ s = 0.694 ms
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What is the energy equivalent of an object with a mass of 1. 05 g? 3. 15 Ă— 105 J 3. 15 Ă— 108 J 9. 45 Ă— 1013 J 9. 45 Ă— 1016 J.
Considering the equivalence between mass and energy given by the expression of Einstein's theory of relativity, the correct answer is the last option: the energy equivalent of an object with a mass of 1.05 kg is 9.45×10¹⁶ J.
The equivalence between mass and energy is given by the expression of Einstein's theory of relativity, where the energy of a body at rest (E) is equal to its mass (m) multiplied by the speed of light (c) squared:
E=m×c²
This indicates that an increase or decrease in energy in a system correspondingly increases or decreases its mass, and an increase or decrease in mass corresponds to an increase or decrease in energy.
In other words, a change in the amount of energy E, of an object is directly proportional to a change in its mass m.
In this case, you know:
m=1.05 kg c= 3×10⁸ m/sReplacing:
E= 1.05 kg× (3×10⁸ m/s)²
Solving:
E= 9.45×10¹⁶ J
Finally, the correct answer is the last option: the energy equivalent of an object with a mass of 1.05 kg is 9.45×10¹⁶ J.
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brainly.com/question/9477556A skier skids to a stop at the bottom of a mountain.
What is the equal and opposite force for the force of the skier's friction pushing on the mountain as
described by Newton's third law?
Answer:
Friction of the mountain on the skier in the opposite direction
Explanation:
answered it on khan academy
Friction of the mountain on the skier in the opposite direction.
What is Newton's third law?A force is a push or a pull that acts upon an object as a results of its interaction with another object. Forces result from interactions.
Forces result from contact interactions (normal, frictional, tensional, and applied forces are examples of contact forces) and other forces are the result of action-at-a-distance interactions (gravitational, electrical, and magnetic forces).
There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces and are the subject of Newton's third law of motion.
Therefore, Friction of the mountain on the skier in the opposite direction.
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(a) Discuss the differences in the band structures of metals, insulators, and semiconductors.
The band structure of a material refers to the arrangement of energy levels or bands that electrons can occupy. The differences in the band structures of metals, insulators, and semiconductors are mainly due to variations in the energy gap between the valence band (VB) and the conduction band (CB).
Metals have a partially filled valence band and an overlapping conduction band. This means that electrons can easily move from the valence band to the conduction band, making metals good conductors of electricity.
Insulators have a large energy gap between the valence band and the conduction band. This gap is usually too large for electrons to bridge, so insulators have very low conductivity.
Semiconductors have a smaller energy gap compared to insulators. This allows some electrons to jump from the valence band to the conduction band when provided with energy, such as heat or light. This property gives semiconductors intermediate conductivity between metals and insulators.
In summary, metals have overlapping energy bands, insulators have a large energy gap, and semiconductors have a smaller energy gap that can be bridged under certain conditions.
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A power station that is being started up for the first time generates 6120 MWh of energy over a 10 hour period. (i) If the rated power at full capacity is 660 MW, calculate how long it takes the power station to reach its full power output. (You may assume a constant increase in power from zero to full power) (ii) State what type of power station can be started up fastest and explain why the start-up times for other types of power station are slower. Explain briefly, how this is relevant to optimising the usage of windfarms. c) What is the Bremsstrahlung effect and how can it be avoided in shielding design? d) Sketch the electromagnetic field output from an antenna, describing in detail the two main regions in the output field.
(i)Therefore, it takes approximately 9.27 hours to reach its full power output.(ii)It is necessary to have quick-start power sources, this helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.(c)The Bremsstrahlung effect needs to be considered to ensure proper radiation protection.(d) The near-field region is characterized by strong electric and magnetic fields while the far-field region represents the radiation zone.
(i) To calculate the time it takes for the power station to reach its full power output, we can use the formula:
Energy = Power × Time
Given that the power station generates 6120 MWh of energy over a 10-hour period and the rated power at full capacity is 660 MW, we can rearrange the formula to solve for time:
Time = Energy ÷ Power
Converting the energy to watt-hours (Wh):
Energy = 6120 MWh × 1,000,000 Wh/MWh = 6,120,000,000 Wh
Converting the power to watt-hours (Wh):
Power = 660 MW × 1,000,000 Wh/MW = 660,000,000 Wh
Now we can calculate the time:
Time = 6,120,000,000 Wh ÷ 660,000,000 Wh ≈ 9.27 hours
Therefore, it takes approximately 9.27 hours (or 9 hours and 16 minutes) for the power station to reach its full power output.
(ii) The type of power station that can be started up fastest is a gas-fired power station. Gas-fired power stations can reach full power output relatively quickly because they use natural gas combustion to produce energy.
In contrast, other types of power stations, such as coal-fired or nuclear power stations, have longer start-up times. Coal-fired power stations require time to heat up the boiler and generate steam, while nuclear power stations need to go through a complex series of procedures to ensure safe and controlled nuclear reactions.
This is relevant to optimizing the usage of windfarms because wind power is intermittent and dependent on the availability of wind. This helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.
(c) The Bremsstrahlung effect is a phenomenon that occurs when charged particles, such as electrons, are decelerated or deflected by the electric fields of atomic nuclei or other charged particles. As a result, they emit electromagnetic radiation in the form of X-rays or gamma rays.
In shielding design, the Bremsstrahlung effect needs to be considered to ensure proper radiation protection. These materials effectively absorb and attenuate the emitted X-rays and gamma rays, reducing the exposure of individuals to harmful radiation.
(d) The electromagnetic field output from an antenna can be represented by two main regions:
Near-field region: This region is closest to the antenna and is also known as the reactive near-field. It extends from the antenna's surface up to a distance typically equal to one wavelength. In the near-field region, the electromagnetic field is characterized by strong electric and magnetic field components.
Far-field region: Also known as the radiating or the Fraunhofer region, this region extends beyond the near-field region.The electric and magnetic fields are perpendicular to each other and to the direction of propagation. The far-field region is further divided into the "Fresnel region," which is closer to the antenna and has some characteristics of the near field, and the "Fraunhofer region," which is farther away and exhibits the properties of the far-field.
The transition between the near-field and the far-field regions is gradual and depends on the antenna's size and operating frequency. The size of the antenna and the distance from it determine the boundary between these regions.
In summary, the near-field region is characterized by strong electric and magnetic fields, while the far-field region represents the radiation zone where the energy is radiated away as electromagnetic waves.
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A point charge is placed at each corner of square with side leanth a. The charges all have same magnitude q. My question, What is the its magnitude in terms of q and a?
Answer:
E = k q / a² (1.3535) (- i ^ + j ^)
E = k q / a² 1.914 , θ’= 135
Explanation:
For this exercise we will use Newton's second law where we must add as vectors
E_total = E₁₂ i ^ + E₁₄ j ^ + E₁₃
Let's look for the value of each term
On the x axis
E₁₂ = k q / a²
On the y axis
E₁₄ = k q / a²
For the charge in the opposite corner we look for the distance
d = √ (a² + a²) = a √2
let's look for the field
E₁₃ = k q / d²
E₁₃ = k q / 2a²
let's use trigonometry to find the two components of this field
cos 45 = E₁₃ₓ / E₁₃
E₁₃ₓ = E₁₃ cos 45
sin 45 = E_{13y} / E₁₃
E_{13y} = E₁₃ sin 45
E₁₃ₓ = k q / 2a² cos 45
E_{13y} = k q / 2a² sin 45
let's find each component of the electric field
X axis
Eₓ = -E₁₂ - E₁₃ₓ
Eₓ = - k q / a² - k q / 2a² cos 45
Eₓ = - k q / a² (1 + cos 45/2)
cos 45 = sin 45 = 0.707
Eₓ = - k q / a² (1 + 0.707 / 2)
Eₓ = - k q / a² (1.3535)
Y axis
E_y = E₁₄ + E_{13y}
E_y = k q / a² + k q / 2a² sin 45
E_y = k q / a² (1 + sin 45/2)
E_y = k q / a² (1.3535)
we can give the results in two ways
E = k q / a² (1.3535) (- i ^ + j ^)
In modulus and angle form, let's use Pythagoras' theorem for the angle
E = √ (Eₓ² + E_y²)
E = k q / a² 1.3535 √2
E = k q / a² 1.914
we use trigonometry for the angle
tan θ = E_y / Eₓ
θ = tan⁻¹ (E_y / Eₓ)
θ = tan⁻¹ (1 / -1)
θ = 45
in the third quadrant, if we measure the angle of the positive side of the x-axis
θ‘= 90 + 45
θ’= 135