Answer:
when x=0 kinetic energy is maximum and potential energy is high
when it is in mean position the potential energy is maximum and vise versa
Explanation:
And x=0 when the pendulum is at highest point when moving like velocity become zero when ball reached highest point
mean position is the point when pendulum comes back to original position
I hope u understand
Three books are at rest, in equilibrium, on a horizontal table as
shown. The weight of each book, which is equal to the force
gravity exerts in the downward direction, is given. What is the
net force on the middle book?
Answer:
Net force = 0
Explanation:
Short answer: if the middle book is not acceleration in any direction, the net force is zero.
Long answer: refer to the attached free-body diagram (FBD) to see why the net force is zero. Skills to draw FBD are essential in solving problems in statics.
Top book exerts -mg (downwards) on the middle book.
Middle book exerts -mg (downwards) on the bottom book.
Total downward force is -mg-mg = -2mg
By Newton's third law, when an object is not in motion, reaction equals action of -2mg in the opposite direction, therefore the reaction (upwards) is +2mg.
This makes the net force of -2mg (downwards) + 2mg (upwards) =0
On a horizontal table, three books are resting and balanced. The net force on the middle book will be equal to zero.
What is equilibrium?Equilibrium is the condition of an object when two or more opposing forces, whether internal, external or a combination of both, act on the body and cancel one another out to maintain the object in the same state as it was. The Latin term for weight or balance, libra, serves as the origin of the word equilibrium.
According to the question :
The net force is 0 if the middle book does not accelerate in any direction.
The Middle book is impacted negatively (downwards) by the top book.
The middle book pulls down on the lower book by -mg.
The total downward force is -2mg = (-mg-mg)
According to Newton's third rule, a reaction when an item is not moving equals an action of -2mg in the opposite direction, hence the reaction (upwards) is a response of +2mg.
Consequently, the net force of -2mg (downwards) + 2mg (upwards) = 0 is created.
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why does a hot air balloon fall when the air inside is not heated
By starting with a falsifiable hypothesis and proceeding to gather data and ensure replicability, a scientist can contribute to the potential formation of a(n)
Answer:
theory
Explanation:
A scientist can contribute to the formation of a theory in a particular subject by conducting research along the line of that subject.
Conducting research requires the formation of a hypothesis and testing the hypothesis by conducting a relevant experiment during which data are gathered, analyzed, and interpreted in order to falsify or accept the hypothesis.
A good experiment must be replicate-able. When the same experiment is repeated by different independent researchers and the same conclusion is arrived at, this could potentially lead to the formation of a theory.
Hence, a scientist can contribute to the formation of a theory by conducting an experiment with replicability in order to test a hypothesis.
Hello Guys! Could u help me with this question. Starting with an initial velocity of 2 m/s, Rohan pressed the accelerator of his car to attain a velocity of 12 m/s in 30s. Then he applies the brakes such that the car comes to rest in the next 15s. Calculate the acceleration of the car in both the cases.
Collaborative learning activities:__________.
A) Can empower students
B) Can give students ownership of their learning
C) Allow students and teachers to become partners in learning
D) Are best facilitated in lecture halls
Answer:
Options A, B as well as C are the correct choices.
Explanation:
Collaborative learning seems to be a circumstance where learning is an educational approach as well as make an effort to understand all this together. Except for personal learning, people participating in this learning draw mostly on competencies and qualifications of each other.This form of learning isn't always linked to the perhaps one given choice. And the response to the above will still be the appropriate one.
3. An electron with a mass of 9.11 X 10^-31 kg is moving at a speed of 2.19 X 10 m/s. What is the kinetic energy of the electron?
Answer:
[tex] 2.18\times 10^{-30} \:J[/tex]
Explanation:
[tex] K.E._{Electron}= \frac{1}{2} mv^2 \\\\
= \frac{1}{2} \times 9.11\times 10^{-31}\times (2.19\times 10)^2 \\\\
=4.555\times 10^{-31}\times 4.7961\times 10^2 \\\\
=4.555\times 10^{-31+2}\times 4.7961 \\\\
=21.8462355\times 10^{-29}\\
=2.18462355\times 10^{-30}\\
=2.18\times 10^{-30} \:J\\[/tex]
Which is the best example of muscular endurance
Answer:
personally I'd say C by do not know if that is the exact answer
Radioisotopes often emit alpha particles, beta particles, or gamma rays. The distance they travel through matter increases in order from alpha to gamma. Each radioisotope has a characteristic half-life, which is the time needed for half of a sample of radioisotope to undergo nuclear decay. Which quality is desirable for a radioisotope that is used for medical imaging of a specific organ
Answer:
It emits alpha and beta particles.
Explanation:
EDG 20
Answer:
the answer is b, calcium-45
Explanation:
Find the force. 10 points. Will give brainliest!
Answer:
8996kg*m/s/s
Explanation:
Given:
a=26m/s/s
m=346kg
Required:
f=?
Formula:
f=m*a
Solution:
f=346kg*26m/s/s
f=8996kg*m/s/s
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{F = 8996 \ Newton}[/tex]
Explanation:
Given:
Mass = m = 346 kg
Acceleration = a = 26 m/s²
Required:
Force = F = ?
Formula:
F = ma
Solution:
F = 346 * 26
F = 8996 Newton
A ray of light is projected into a glass tube that is surrounded by air. The glass has an index of refraction of 1.50 and air has an index of refraction of 1.00. At what minimum angle will light in the glass tube be totally reflected at the glass/air interface?
Answer:
θ = 41.8º
Explanation:
This is an internal total reflection exercise, the equation that describes this process is
sin θ = n₂ / n₁
where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂
θ = sin⁻¹ n₂ / n₁
let's calculate
θ = sin⁻¹ (1.00 / 1.50)
θ = 41.8º
Resistor R1 and R2 are connected in parallel to an emf source that has negligible internal resistance. What happens to the current through R1 when the third resistor R3 is connected parallel with R1?
The current does not change.
All three resistors are connected directly to the power source, and are unaware of each other.
The maximum wavelength For photoelectric emissions in tungsten is 230 nm. What wavelength of light must be use in order for electron with maximum energy of 1.5ev to be ejection
Answer:
λ = 1.8 x 10⁻⁷ m = 180 nm
Explanation:
First we find the work function of tungsten by using the following formula:
∅ = hc/λmax
where,
∅ = work function = ?
h = Plank's Constant = 6.626 x 10⁻³⁴ J.s
c = speed of light = 3 x 10⁸ m/s
λmax = maximum wavelength for photoelectric emission = 230 nm
λmax = 2.3 x 10⁻⁷ m
Therefore,
∅ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(2.3 x 10⁻⁷ m)
∅ = 8.64 x 10⁻¹⁹ J
Now we convert Kinetic Energy of electron into Joules:
K.E = (1.5 eV)(1.6 x 10⁻¹⁹ J/1 eV)
K.E = 2.4 x 10⁻¹⁹ J
Now, we use Einstein's Photoelectric Equation:
Energy of Photon = ∅ + K.E
Therefore,
Energy of Photon = 8.64 x 10⁻¹⁹ J + 2.4 x 10⁻¹⁹ J
Energy of Photon = 11.04 x 10⁻¹⁹ J
but,
Energy of Photon = hc/λ
where,
λ = wavelength of light = ?
Therefore,
11.04 x 10⁻¹⁹ J = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ
λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(11.04 x 10⁻¹⁹ J)
λ = 1.8 x 10⁻⁷ m = 180 nm
Imagine that your standing on a beach but cannot swim. Your friend encourages you to walk into the surf zone created by incoming deep-water waves that have a wavelength of 30 meters. Would it be safe to walk out to where the waves are breaking? Explain how you arrived at your answer.
Answer:
It would not be safe to walk out to where waves are breaking due to the effect of rip currents
Explanation:
The water depth in the surf zone is between 5 to 10 meters deep and with a wavelength of 30 meters, the speed of the wave is considerably fast such that control for safety may be difficult
Also the speed of the wave is directly related to the depth of the water which means that where the wave described above is fast as well as the rip current, also the water depth is expected to be considerable for a non swimmer
It is best to seek for sign post regarding safe areas and do not go into the water where there are no lifeguards or marked safe zones.
It won't be safe to walk out to where the waves are breaking.
This is because the wavelength is 30 meters which is a characteristic of
areas with significant water depth in the range of 5-11 meters.Under these
conditions the waves are usually very fast and may get swept with the
current from the water waves when trying to run from it.
It is recommended that we stay in areas where the depth is noted as not
being much and should always seek help and clarity from the life guards so
as to prevent drowning and death.
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A long, rigid conductor, lying along an x axis, carries a current of 5.0 A in the negative x direction. A magnetic field B: is present, given by B: ???? 3.0iˆ ???? 8.0x2jˆ, with x in meters and B: in milliteslas. Find, in unit-vector notation, the force on the
Answer:
Explanation:
magnetic field B = (3 i + 8 x 2 j )x 10⁻³ T
= (3 i + 16 j )x 10⁻³ T
L = - i ( unit length of conductor )
Force F = I ( L x B ) , I is current
= 5 [ - i x ( 3i + 16 j ) 10⁻³]
= 5 ( - 16 k ) x 10⁻³
F = - 80 x 10⁻³ k
Is The force of friction always opposite to the motion?
Answer:
Friction force always acts tangent to the surface at points of contact. Friction force acts opposite to the direction of motion.
Explanation:
CAN SOMEONE HELP ME PLEASE!? After chasing its prey, a cougar leaves skid marks that are 236 m in length. Assuming the cougar skidded to a complete stop with a constant acceleration of -2.87 m/s^2, identify the speed of the cougar before it began to skid.
Answer:
u=36.8m/s
Explanation:
because of the acceleration is a constant acceleration we can use one of the "SUVAT" equations
u^2=v^2-2ā*s. where:
u^2 stands for intial velocity
v^2 stands for final velocity
since the cougar skidded to a complete stop the final velocity is zero.
u^2=v^2-2ā*s
u^2=(0)^2 -2(-2.87 m/s^2)*236 m
u^2=0+5.74m/s^2* 236m
u^2=1354.64m^2/s^2
u=√1354.64m^2/s^2
u=36.8m/s (approximate value)
when ever the acceleration is constant you can use one of the following equation to find the required value.
1. v = u + at. (no s)
2. s= 1/2(u+v)t. (no ā)
3. s=ut + 1/2at^2. ( no v)
4. v^2=u^2 + 2āS. (no t). 5. s= vt - 1/2at^2. (no u)
a truck is moving with a certain uniform velocity. it is accelerated uniformly by 0.75 m/s^2.after 20 seconds, the velocity becomes 72 km/h. find the initial velocity
Answer:
[tex]\boxed{V_{i} = 5\ m/s}[/tex]
Explanation:
Given:
Acceleration = a = 0.75 m/s²
Time = t = ?
Final Velocity = [tex]V_{f}[/tex] = 72 km/hr = 20 m/s
Required:
Initial Velocity = [tex]V_{i}[/tex] = ?
Formula:
a = [tex]\frac{V_{f}-V_{i}}{t}[/tex]
Solution:
For [tex]V_{i}[/tex] the formula becomes:
[tex]V_{i} = V_{f}-at[/tex]
[tex]V_{i}[/tex] = 20 - (0.75)(20)
[tex]V_{i}[/tex] = 20 - 15
[tex]V_{i}[/tex] = 5 m/s
In Case: If you want it in km/hr:
[tex]V_{i}[/tex] = 5 * 3.6
[tex]V_{i}[/tex] = 18 km/hr
Answer:
5 m/s
Explanation:
acceleration = 0.75 m/s²
time = 20 s
final velocity = 72 km/h = 20 m/s
initial velocity = ?
Apply formula for initial velocity.
[tex]u=-at+v[/tex]
[tex]\sf a=acceleration\\t=time\\v=final \: velocity\\u=initial \: velocity[/tex]
Solve for u.
[tex]u=-(0.75)(20)+ 20[/tex]
[tex]u=-15+20[/tex]
[tex]u= 5[/tex]
A nonrenewable resource
Answer:
It is a finite resource.
Explanation:
A nonrenewable resource is a natural substance that is not replenished with the speed at which it is consumed. Fossil fuels such as oil, natural gas, and coal are examples of nonrenewable resources.
Answer:
Coal, oil, natural gas.
Explanation:
Non renewable resource -A non-renewable resource (also called a finite resource) is a natural resource that cannot be readily replaced by natural means at a quick enough pace to keep up with consumption.
Coal, oil, and natural gas are all examples of non-renewable resources and cannot be readily replaced to keep up with consumption.
what nuclear fission and nuclear fusion have in common? A. They’re both used in power plants B. they have less mass than their reactants C. they start with the same reactants D. their products have more mass than their reactants
Answer:
B. they have less mass than their reactants
Explanation:
In both nuclear fission and nuclear fusion, the products have less mass than their reactants. So, option B is correct.
What is meant by nuclear reaction ?Nuclear reaction is defined as the reaction that involves the collision between one or more atomic nuclei and a highly energetic subatomic particle to produce one or more nuclei along with the emission of a large amount of energy.
Here,
Nuclear fission and fusion are two types of nuclear reactions that involves the production of large amount of energy from atomic nuclei.
Nuclear fission is the nuclear reaction in which a heavier nucleus is split into two or more lighter nuclei, under radioactive condition, with the release of a massive amount of energy.
Nuclear fusion is the nuclear reaction in which two or more lighter nuclei nuclei fuse together under radioactive condition and forms a heavier nuclei and by releasing a large amount of energy.
In both nuclear fission and nuclear fusion, there occurs a release of large amount of energy. This is because most of the mass of the reactants is converted into energy which is known as the mass-energy. So the products of these nuclear reactions will have lesser mass than their reactants.
Hence,
In both nuclear fission and nuclear fusion, the products have less mass than their reactants.
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The total mass of eight identical
building blocks is 31.52 kg. Find the
mass of 1 block.
Answer:
3.94
Explanation:
divide total mass by the number of blocks since they are identical
Answer:
3.94
Explanation:
You want to find the mass of one block. Since we know there is 8 blocks with the same mass, you can divide the total mass by 8 since the mass is equally distributed within the 8 blocks
Show that energy dissipated due to motion of a conductor in the magnetic field is due to mechanical energy.
Explanation:
let us use the explanation below to get the intuition so desired;
According to Faraday's law of electro magnetic induction, when ever a coil/conductor is made to rotate in a magnetic field, voltage or emf is created and current is produced, in the long run energy has be produced or converted.
The conversion of this energy is made possible by the motion of the coil/conductor is the magnetic field, just by the motion of the conductor cutting through the magnetic field, thus creating electro motive force(E.M.F) hence producing current, and ultimately energy is created
The Si unit of potential difference is a) volt b) JA⁻¹s⁻¹ c)JC⁻¹ d) All the above
Answer:
a) Volt
Explanation:
The standard metric unit on electric potential difference is the volt.
answer
all of the above
explanation
as we know that the si unit of potential difference is volt
which is equal to j/c and j/c is equal to j/a.s so the correct answer is all of the above
Assignment: Ultrasound and Infrasound Research Exploration Ultrasound and infrasound are categories of sound with different frequencies. These categories of sound can be used for a variety of different applications. In this research assignment, you will take a look at the industrial applications of ultrasound and infrasound. Your essay should do the following things: • Define and describe in detail (and in your own words) ultrasound and infrasound • Describe how ultrasound and infrasound are used in specific industrial applications and provide detailed examples. When conducting your research, remember to gather information from multiple sources. Start your research by defining ultrasound and infrasound. Then find ideas about industrial applications. The essay should be about 350-450 words, which is 1-1.5 typed pages, double-spaced, using 12-pt. font. Check the rubric to review how you will be graded for this assignment. plz no funny answers
Answer:
Infrasound vs. Ultrasound: Infrasound is sound that is below the lower limit of human hearing, below 20 Hz, and ultrasound is above the upper limit of human hearing, above 20,000 Hz. Individuals use infrasound - this recurrence run for checking seismic tremors and volcanoes, graphing rock and oil developments underneath the earth. Infrasound is described by a capacity to get around hindrances with little scattering.
For instance, a few creatures, for example, whales, elephants and giraffes convey utilizing infrasound over significant distances. Torrential slides, volcanoes, seismic tremors, sea waves, water falls and meteors produce infrasonic waves. Symptomatic ultrasound, additionally called sonography or demonstrative clinical sonography, is an imaging technique that utilizes high-recurrence sound waves to create pictures of structures inside your body. The pictures can give important data to diagnosing and treating an assortment of ailments and conditions.
Explanation:
idk how many words this is but its a start for u to add on to and i hope this helps and its in my own words - pls mark me brainiest
Answer:
Ultrasound vs. Infrasound Research Exploration
Beyond the limit of human hearing, ultrasound is above 20,000 Hz. Under the limit of human hearing, infrasound is below 20 Hz. Individuals use infrasound - this recurrence run for checking seismic tremors and volcanoes as well as graphing rock and oil developments beneath the earth. Infrasound is described by a capacity to get around hindrances with little scattering.
For instance, creatures like whales, elephants and giraffes convey utilizing infrasound over significant distances. Torrential slides, volcanoes, seismic tremors, sea waves, waterfalls and meteors produce infrasonic waves. Symptomatic ultrasound, additionally called sonography or demonstrative clinical sonography, is an imaging technique that utilizes high-recurrence sound waves to create pictures of structures inside your body. The pictures can give important data to diagnosing and treating an assortment of ailments and conditions.
(Not turned in yet, but this is what i have so far. Good luck 8th graders <33)
-Sav xx
please help me to solve the problem
?cm=1m
A square loop 24.0 cm on a side has a resistance of 6.10Ω. It is initially in a 0.665-T magnetic field, with its plane perpendicular to magnetic field B but is removed from the field in 40.0ms. Calculate the electric energy dissipated in this process.
Answer:
[tex]E=6.01\times 10^{-3}\ J[/tex]
Explanation:
It is given that,
Side of a square loop, l = 24 cm = 0.24 m
Resistance of loop, R = 6.1 ohms
Initial magnetic field is 0.665 T and final magnetic field is 0 as the field is removed in 40 ms
We need to find the electrical energy dissipated in this process.
Due to change in magnetic field, the loop will induce a voltage. The induced voltage is given by :
[tex]V=-\dfrac{dB}{dt}\\\\V=\dfrac{BA}{t}[/tex]
If I is induced current then,
[tex]V=IR[/tex]
[tex]I=\dfrac{V}{R}\\\\I=\dfrac{BA}{tR}[/tex]
Power is given by voltage times current. So,
[tex]P=\dfrac{(BA)^2}{(t^2R)}[/tex]
Now, energy is given by the product of power and time. So,
[tex]E=\dfrac{(BA)^2}{(t^2R)}\times t\\\\E=\dfrac{(BA)^2}{(tR)}[/tex]
Now putting all the values in above formula. So,
[tex]E=\dfrac{(0.665\times (0.24)^2)^2}{(40\times 10^{-3}\times 6.1)}\\\\E=6.01\times 10^{-3}\ J[/tex]
So, the electrical energy of [tex]6.01\times 10^{-3}\ J[/tex] is dissipated in this process.
The electrical energy dissipated throughout this process will be "6.01 × 10⁻³ J".
Magnetic fieldAccording to the question,
Square loop's side, l = 24 cm or,
= 0.24 m
Loop's resistance, R = 6.1 ohms
Initial magnetic field = 0.665 T
Final magnetic field = 0
We know the relation,
→ V = - [tex]\frac{dB}{dt}[/tex]
= [tex]\frac{BA}{t}[/tex]
Also we know,
Current, V = IR
I = [tex]\frac{V}{R}[/tex]
= [tex]\frac{BA}{tR}[/tex]
Now, Energy, E = [tex]\frac{(BA)^2}{t^2R}[/tex] × t or,
= [tex]\frac{(BA)^2}{tR}[/tex]
By substituting the values,
= [tex]\frac{(0.665\times (0.24)^2)^2}{40\times 10^{-3}\times 6.1}[/tex]
= 6.01 × 10⁻³ J
Thus the response above is correct.
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Which is one piece of evidence of seafloor spreading? help :(
Answer:
Mid ocean ridges are evidence of sea floor spreading as tectonic movement opens a gash or "fault" in the ocean floor.
Answer:
Eruptions of molten material, magnetic stripes in the rock of the ocean floor, and the ages of the rocks themselves; this evidence led scientists to look again at Wegener's hypothesis of continental drift.
Which of the following statements are true? (mark all that apply)
A) Adaptive optics corrects for atmospheric distortion by following the distortion of a bright star, possibly an artificial star created by a laser, and rapidly changing the shape of a mirror using computer-controlled actuators to compensate for the distortion.
B) Improvements in technology will eventually allow the entire electromagnetic spectrum to be observed from high mountaintop observatories.
C) X rays from astronomical objects can only be detected from telescopes in space or in high altitude rockets.
D) The best observing sites for optical telescopes are atop remote mountains.
E) Radio telescopes must be carried to high altitudes by balloons in order to detect this type of radiation.
Answer:
The answer(s) for this question are as followed: A, C, & D
Explanation:
I hope this helped, let me know if i missed any.
Hypothetically speaking, if an object were located at the center of the Earth, the gravitational force on that object due to the surrounding Earth, assuming matter is uniformly distributed, would have which of the following values?
a) The force would be approximately the same value as if the object were on the surface of the Earth.
b) The force would be much greater than the value if the object were on the surface of the Earth.
c) The force would be somewhat less than the value if the object was on the surface of the Earth, but it would be greater than zero newtons.
d) The force would be zero newtons.
Answer:
D. ) The force would be zero newtons
Explanation:
Because
If you are at the center of the earth, gravity is zero because all the mass around you is pulling "up" (every direction there is up!)
So F=mg so if g is zero F is also zero
Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b), and all other quantities remained the same, the magnetic field inside the solenoid would
Answer:
The magnetic field remains the same.
Explanation:
If a solenoid has length L, N windings, and radius b, then the magnetic field inside the solenoid is given by :
[tex]B=\mu_o NI[/tex]
[tex]\mu_o[/tex] is magnetic permeability
If the radius of the solenoid were doubled and all other quantities remained the same, the magnetic field inside the solenoid would remains the same as it is independent of the radius of the solenoid.
The magnetic field perpendicular to a single 13.2-cm diameter circular loop of copper wire decreases uniformly from 0.670 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation? (rhoCu = 1.68 x 10-8 Ω.m)
Answer:
5.23 C
Explanation:
The current in the wire is given by I = ε/R where ε = induced emf in the wire and R = resistance of wire.
Now, ε = -ΔΦ/Δt where ΔΦ = change in magnetic flux = AΔB and A = area of loop and ΔB = change in magnetic field intensity = B₂ - B₁
B₁ = 0.670 T and B₂ = 0 T
ΔB = B₂ - B₁ = 0 - 0.670 T = - 0.670 T
A = πD²/4 where D = diameter of circular loop = 13.2 cm = 0.132 m
A = π(0.132 m)²/4 = 0.01368 m² = `1.368 × 10⁻² m²
ε = -ΔΦ/Δt = -AΔB/Δt = -1.368 × 10⁻² m² × (-0.670 T)/Δt= 0.9166 × 10⁻² Tm²/Δt
Now, the resistance R of the circular wire R = ρl/A' where ρ = resistivity of copper wire = 1.68 x 10⁻⁸ Ω.m, l = length of wire = πD and A' = cross-sectional area of wire = πd²/4 where d = diameter of wire = 2.25 mm = 2.25 × 10⁻³ m
R = ρl/A' = 1.68 x 10⁻⁸ Ω.m × π × 0.132 m÷π(2.25 × 10⁻³ m)²/4 = 0.88704/5.0625 = 0.1752 × 10⁻² Ω = 1.752 × 10⁻³ Ω
So, I = ε/R = 0.9166 × 10⁻² Tm²/Δt1.752 × 10⁻³ Ω
IΔt = 0.9166 × 10⁻² Tm²/1.752 × 10⁻³ Ω = 0.5232 × 10 C
Since ΔQ = It = 5.232 C ≅ 5.23 C
So the charge is 5.23 C
The induced emf through wire depends on the current flow (indirectly with charge flow as well).
The value of charge moving past a point in the coil during its operations is 5.23 C.
What is the magnetic field?The region in a space where a particle experiences some magnetic force, is known as the magnetic field.
Given data -
The diameter of the circular loop is, d = 13.2 cm = 0.132 m.
The change in magnetic field strength is, ΔB = 0.670 T.
The new diameter of the wire is, d' = 2.25 mm = 2.25 × 10³ m.
The resistivity of the wire is, [tex]\rho = 1.68 \times 10^{-8} \;\rm \Omega.m[/tex].
The current in the wire is given by the following expression,
I = ε/R
Here,
ε is the induced emf in the wire.
R is the resistance of the wire.
And the expression for the induced emf of the wire is given as,
ε = -ΔΦ/Δt
Here,
ΔΦ is the change in magnetic flux. And its expression is,
ε = A × ΔB
Here,
A is the area of the loop. And its value is, A = πd²/4.
Solving as,
A = π(0.132 m)²/4
A = 0.01368 m²
A = `1.368 × 10⁻² m²
Now, calculating the induced emf as,
ε = ΔΦ/Δt
ε = A × ΔB/Δt
ε = 1.368 × 10⁻² m² × (0.670 T)/Δt
ε = 0.9166 × 10⁻² Tm²/Δt
Now, the resistance R of the circular wire is,
R = ρ × L/A'
Here,
L is the length of the wire and its value is. L = πd .
And A' is the new cross-sectional area of wire,
A' = πd'²/4
So, the resistance is,
R = ρ × L/A'
R = 1.68 x 10⁻⁸ ×( π × 0.132 m) ÷ π(2.25 × 10⁻³ m)²/4 =
R = 0.88704/5.0625
R = 0.1752 × 10⁻² Ω
R = 1.752 × 10⁻³ Ω
Now, the current flow (I) in the wire is given as,
I = ε/R
I = 0.9166 × 10⁻² Tm²/Δt1.752 × 10⁻³ Ω
And obtaining the value of charge from the expression of current as,
Q = IΔt
Q = 0.9166 × 10⁻² Tm²/1.752 × 10⁻³ Ω
Q = 0.5232 × 10 C
Q = 5.23 C
Thus, we can conclude that the value of charge moving past a point in the coil during its operations is 5.23 C.
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