A current I starts at z = -~ and flows up the z-axis as a linear filament until its hits an origin-centered sphere of radius R. The current spreads out uniformly over the surface of the sphere and flows up lines of longitude from the south pole to the north pole. The recombined current flows thereafter as a linear filament up the z-axis to z = +0. (a) Find the current density on the sphere. (b) Use explicitly stated symmetry arguments and Ampère's law in integral form to find the magnetic field at every point in space. (c) Check that your solution satisfies the magnetic field matching conditions at the surface of the sphere.
Answers
J = I / (4πR²),
The magnetic field inside the sphere isB(r) = μ0 I / (2πr),
The magnetic field Outside the sphere isB(r) = μ0 I r² / (2 R³),
The magnetic field is continuous across the surface of the sphere.How to find magnetic field on spherical surface using Ampère's law?(a) The current density on the sphere can be found by dividing the total current by the surface area of the sphere.
The total current is equal to the current flowing through the linear filament, which is given by I. The surface area of the sphere is given by 4πR². Therefore, the current density on the sphere is:J = I / (4πR²)
(b) Due to the symmetry of the problem, the magnetic field will have no φ-component, and will only depend on the radial distance r and the polar angle θ.
By Ampère's law,
The magnetic field at a point P inside the sphere of radius R can be found by integrating the current density J over a circular path C around the z-axis passing through P:
∮C B · dl = μ0 Ienc
where,
B is the magnetic field, dl is the infinitesimal element of path length along C, μ0 is the permeability of free space, and Ienc is the current passing through any surface bounded by C.Since the current is distributed uniformly over the surface of the sphere, we can take a surface S with the same circular path C as its boundary.
Then, Ienc is equal to the total current passing through the sphere, which is equal to I.
By symmetry,
The magnetic field will be perpendicular to the circular path C at every point, and its magnitude will only depend on the distance r from the z-axis. Therefore, we can writeB = B(r) ẑ,
where,
ẑ is the unit vector in the z-direction. The integral can be evaluated as:B(r) ∫C dl = B(r) 2πr = μ0 I
Solving for B(r), we obtain:B(r) = μ0 I / (2πr)
This is the magnetic field at every point in space inside the sphere.(c) At the surface of the sphere, the magnetic field must be continuous across the boundary.
Therefore, we need to evaluate the magnetic field both inside and outside the sphere and make sure they match at r = R.
For r < R, we have:
B(r) = μ0 I / (2πr)
For r > R, the magnetic field is due to the current flowing on the surface of the sphere.
By Ampère's law,
we can take a circular path C of radius r centered on the z-axis, passing through the point P outside the sphere, and evaluate the magnetic field due to the current passing through the surface bounded by C. Since the current is flowing up lines of longitude, the current passing through the surface bounded by C is equal to the current passing through a circular disk of radius r on the surface of the sphere. The current density on the disk is:J = I / (4πR²),
The current passing through the disk is:Ienc = J π r²
Therefore, we have:B(r) ∫C dl = B(r) 2πr = μ0 Ienc
Solving for B(r), we obtain:B(r) = μ0 I r² / (2 R³)
At r = R, the magnetic field is:B(R) = μ0 I / (2πR) = μ0 I R / (2πR²) = μ0 J R
which is the same as the magnetic field due to the current density on the surface of the sphere.
Therefore, the magnetic field is continuous across the surface of the sphere, and our solution satisfies the magnetic field matching conditions.
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Related Questions
______is the rate of change of velocity. A,speed. B,distance. C,acceleration. D,force
Answers
Explanation:
c) aceleración
according to this passage when making healthcare decisions, how should a person approach the decision making process
Answers
Answer:
What is your name?
Explanation:
no bro I don't know I am New of this app so I don't know
if a certain star emits most intensely in the visible region of the spectrum, a cooler star would emit mostly in what part of the spectrum
Answers
A cooler star would emit mostly in infrared range of the spectrum.
Emission of high temperature starsHigh temperature stars like the Sun, which are approximately 6000 K at the surface, emit most of their radiation at visible wavelengths.
Emission of the cooler starsIn stark contrast to high temperature stars, the cooler stars emit most of their radiations in the infrared (IR) range.
Thus, we can conclude that, a cooler star would emit mostly in infrared range of the spectrum.
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It takes Miss Slotman 4 seconds to go from a speed of 3 m/s to a speed of 10 m/s. What is
her acceleration?
PLS HELP!!!! ASAP:(
Answers
Answer:
so to find the acceleration we divide the change in velocity by the time taken for it so intial velocity was 3m/s and final velocity is 10m/s. we substract 3 from 10 to get the change in velocity ie 10m/s -3m/s = 7m/s. now decide this by the time taken for it that is 4 sec as given. acceleration is 7/4 = 1.75m/s^2
What distance is required for a train
to stop if its intial Velocity is 23 m/s
and its deceleration is 0.25m/s (Assume the train decelerates at a constant rate.)
Answers
Explanation:
what is time in this question
A 1500kg car moves foward with 30kg•m/s of momentum. What is its velocity
Select one
•-1470m/s
•0.02m/s
•45,000m/s
•-50m/s
Answers
Answer:
v = 30 /1500= 0.02 m/s
................
What is the height to which the spans rise when they buckle
Answers
Assuming each concrete span is half the length of the bridge, so 195 m
ΔL = αLΔT,
where,
ΔL: change in length
α: coeff. of thermal expansion
L: current original length
ΔT: change in temperature
We need to look at each span individually.
Let's fill in the variables we know:
L = 195 m
α = 1.2*10^-5 /C
ΔT = 20 C
ΔL = (1.2*10^-5)(195)(20)
ΔL = 0.0468 m, this is how much each span expands.
Now, we can form a triangle with the original length of each span, the new length of each span, and the rise due to buckling.
L0 = 195
Ln = 195 + 0.0468 = 195.0468
Now that we have two of the three sides of the triangle, we can solve for the last side, h.
Pythagorean theorem:
195^2 + h^2 = 195.0468^2
Solving for h,
h = 4.272 m
youa re on topa. building that is 75 m tall. you toss a ball straight up with a velocity of 33.8 m/as. how high does the ball travel. it goes up and then falls down to the ground below. how much time is it in the air
Answers
The ball will travel up to a height of 44.89 m. The ball will be in the air for 8.6 seconds. In this problem, the ball is thrown from a height of 75 m. The initial velocity of the ball is 33.8 m/s.
We have to calculate how high the ball travels and for how long it remains in the air.
To find the maximum height that the ball attains,
we can use the formula: h = u^2/2g
Where h is the maximum height, u is the initial velocity and g is the acceleration due to gravity which is equal to 9. 81 m/s^2.Substituting the values,
we get: h = (33.8 m/s)^2/(2 × 9.81 m/s^2)
h ≈ 44.89 m
Therefore, the ball will travel up to a height of approximately 44.89 m.
To find how long the ball is in the air, we can use the formula :t = 2u/g
where t is the time taken to reach maximum height.
substituting the values, we get :t = 2 × 33.8 m/s / 9.81 m/s^2t ≈ 6.87 s
Therefore, the ball is in the air for approximately 6.87 s to reach maximum height.
As the ball falls down to the ground, the total time in the air will be twice this value, which is approximately 8.6 seconds.
Velocity (u) = 33.8 m/s
Acceleration (g) = 9.81 m/s^2
Maximum height (h) = u^2/2g =
(33.8 m/s)^2/(2 × 9.81 m/s^2) ≈ 44.89 m
Time to reach maximum height (t) = 2u/g = 2 × 33.8 m/s / 9.81 m/s^2 ≈ 6.87 s
Total time in the air = 2t = 2 × 6.87 s ≈ 8.6 s.
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a 5.2kg bowling ball is accelerated from rest to a velocity of 12 m/s as the bowler covers 5.0m of approach before releasing the ball. what force is exerted on the ball during this time?
Answers
Answer:
74.88N
Explanation:
From the question,
F = ma................... Equation 1
Where F = force exerted on the ball, m = mass of the ball, a = acceleration
But,
v² = u²+2as.............. Equation 2
Where v = final velocity, u = initial velocity, s = distance.
Given: v = 12 m/s, u = 0 m/s (from rest), s = 5.0 m
Substitute into equation 2 and solve for a
12² = 0²+2×a×5
144 = 10a
10a = 144
a = 144/10
a = 14.4 m/s²
Also Given: m = 5.2 kg,
Substitute into equation 1
F = 5.2×14.4
F = 74.88 N
Hence the force exerted on the ball is 74.88 N
the steel beams of the space needle rise to a height of 180 meters on a 0.0°c winter day. how much taller is the space needle on a day when the air temperature is 20°c?
Answers
the Space Needle would be approximately 0.0432 meters (or 4.32 centimeters) taller on a day when the air temperature is 20°C compared to a 0°C winter day.
When an object is heated, its volume (and therefore its height) will increase due to the expansion of the material. The amount of expansion depends on the coefficient of thermal expansion of the material and the temperature change.
The coefficient of thermal expansion of steel is approximately \(1.2 x 10^-5\)per degree Celsius. This means that for every degree Celsius increase in temperature, the steel will expand by \(1.2 x 10^-5\) of its original size.
To calculate the increase in height of the Space Needle, we can use the following formula:
\(Δh = h0 * α * ΔT\\\)
Where:
Δh = increase in height
h0 = original height (180 meters)
α = coefficient of thermal expansion for steel (\(1.2 x 10^-5\) per degree Celsius)
ΔT = temperature change (20°C - 0°C = 20°C)
Substituting the values into the formula, we get:
\(Δh = 180 * 1.2 x 10^-5 * 20\\\)
Δh = 0.0432 meters
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Calculate the wavelength of the first harmonic for a guitar string that is 1 meter long:
Answers
For a guitar string that is 1 meter long, the wavelength of the first harmonic is 2 meters.
The formula for calculating the wavelength of the first harmonic for a guitar string is:
Wavelength = 2 * String length / First harmonic
Given that the guitar string is 1 meter long and we want to calculate the wavelength of the first harmonic, we can substitute these values into the formula as follows:
Wavelength = 2 * 1 meter / 1
Wavelength = 2 meters
Therefore, the wavelength of the first harmonic for a guitar string that is 1 meter long is 2 meters.
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The force of electrostatic repulsion between two small positively charged objects, A and B, is 3.6 x 10⁻⁵ N when AB = 0.12m. What is the force of repulsion if AB is increased to 0.24 m
Answers
Given data:
* The electrostatic force of repulsion between the charged bodies in the initial state is,
\(F=3.6\times10^{-5}\text{ N}\)* The distance between the charged bodies in the initial state is,
\(d=0.12\text{ m}\)* The distance between the charged bodies in the final state is,
\(\begin{gathered} d^{\prime}=0.24\text{ m} \\ d=2\times0.12 \\ d^{\prime}=2d \end{gathered}\)Solution:
According to Coulomb's law, the electrostatic force of repulsion between the charged bodies in the initial state is,
\(F=\frac{kq_1q_2}{d^2}\)where k is the electrostatic force constant, q_1 is the charge on the first charged body and q_2 is the charge on the second charged body,
The electrostatic force of repulsion between the charged bodies in the final state is,
\(\begin{gathered} F^{\prime}=\frac{kq_1q_2}{(2d)^2} \\ F^{\prime}=\frac{kq_1q_2}{4d^2} \\ F^{\prime}=\frac{1}{4}\times\frac{kq_1q_2}{d^2} \\ F^{\prime}=\frac{F}{4} \end{gathered}\)Substituting the known values,
\(\begin{gathered} F^{\prime}=\frac{3.6\times10^{-5}}{4} \\ F^{\prime}=0.9\times10^{-5}\text{ N} \end{gathered}\)Thus, the electrostatic force of repulsion between the charged bodies in the final state is,
\(\text{0}.9\times10^{-5}\text{ N}\)The eyepiece of a compound microscope has a focal length of 2.50 cm and the objective has a focal length of 1.60 cm. The two lenses are separated by 15.0 cm. The microscope is used by a person with normal eyes (near point at 25 cm). What is the angular magnification of the microscope
Answers
The angular magnification of the microscope is 78.125.
What is angular magnification?the ratio of the angle at the eye that an optical instrument's image occupies to the angle at the eye that an object occupies while not being viewed through an optical instrument is called as angular magnification.
Thus we can calculate it as:
focal length of objective lens, fo = 1.6 cmfocal length of the eyepiece, fe = 2.5 cmDistance between the lenses, L = 15 cmLeast distance of distinct vision for normal eye, d = 25 cmThe formula for the magnification of the compound microscope is given by
\(M = - \frac{(L-f{e} )d}{fa fe}\)
\(M = - \frac{(15-2.5 )25}{(1.6) 2.5}\)
M = - 78.125
Thus, the magnification of the compound microscope is 78.125.
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Ammeters must be connected in _____ with the circuit
A) parrellel
B) series
C) vertical
D) hortizontal
Answers
Ammeters must be connected in series with the circuit in order to accurately measure the current flowing through the circuit. When an ammeter is connected in parallel with a circuit, it creates a low-resistance path, which can alter the current in the circuit and give inaccurate readings.
When an ammeter is connected in series, it becomes a part of the circuit and allows the current to flow through it. This way, the ammeter measures the actual current in the circuit, without altering it.
It is important to note that ammeters should only be connected in series with a circuit that is properly designed and has the necessary safety measures in place. Incorrectly connecting an ammeter can create a hazard and damage the equipment. Therefore, it is important to follow proper procedures and safety guidelines when using ammeters to measure electrical current.
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A book is on the table. If the weight of the book is 25 newtons, what is the magnitude and direction of the normal force?A.2.5 newtons in the downward directionB.2.5 newtons in the upward directionC.25 newtons in the upward directionD.25 newtons in the downward directionE.25 newtons perpendicular to the gravitational force
Answers
The normal force has a 25 N force magnitude and an upward force direction.
The force the book exerts on the table is downward-directed and equal to its weight, which is 25 N.
According to Newton's third law, every force an object A applies to an object B is balanced out by an equally strong force applied in the opposite direction to object A.
The book is object A in this instance, while the table is object B. According to Newton's third law, the table pulls on the book with a force that is both equal to and opposite to that of the force exerted by the table. As a result, the normal force's magnitude is the same as the weight of the book (25 N), while its direction is opposite.
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The magnetic field lines due to a straight, current-carrying wire are __________.
Answers
The Magnetic field lines around a straight conductor carrying current are concentric circles whose centres lie on the wire.
If tight scissors have an efficiency of 50 percent, half of your work is wasted due to _____________________
Answers
If tight scissors have an efficiency of 50 percent, half of your work is wasted due to mechanical losses or inefficiencies.
Efficiency is a measure of how effectively a device or system converts input energy into useful output energy. In this case, the efficiency of tight scissors being 50 percent means that only half of the input energy you apply to the scissors is converted into useful output energy, while the other half is lost due to various factors.
Mechanical losses or inefficiencies in scissors can occur for several reasons, including friction, imperfect cutting edges, and deformation of the materials. When you squeeze the handles of the scissors, the energy you apply is not entirely transferred to the cutting action. Some of the energy is dissipated as heat due to friction between the blades, pivot point, and other moving parts. Additionally, if the scissors have dulled or damaged edges, more energy is required to cut through materials, resulting in increased inefficiency.
The wasted energy that is not utilized for cutting is typically converted into heat or sound energy, which does not contribute to the desired output of the scissors.
Therefore, due to mechanical losses or inefficiencies in the scissors, half of the work you apply is wasted, resulting in a 50 percent efficiency. This means that only half of your effort is effectively utilized for cutting, while the other half is lost as non-useful energy.
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when classifying the 36 cells into their individual phases of mitosis, which phase had the highest representation of cells? (From the table on page 3)
Metaphase
Interphase
Prophase
Answers
When classifying the 36 cells into their individual phases of mitosis ,Inter phase had the highest representation of cells .So option B is correct.
Pro phase is the first phase of mitosis, and it is when the chromosomes condense and become visible. The nuclear envelope breaks down, and the spindle fibers form.
Meta phase is the second phase of mitosis, and it is when the chromosomes line up along the spindle fibers. The chromosomes are then pulled apart by the spindle fibers.
Ana phase is the third phase of mitosis, and it is when the chromosomes are pulled to opposite poles of the cell. The cell then begins to divide.
Telophase is the final phase of mitosis, and it is when the cell divides into two daughter cells. The chromosomes uncoil, and the nuclear envelope reforms.Therefore option B is correct.
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A force of 50 N was necessary to lift a rock. A total of 150 J of work was done. How far was the rock lifted?
Answers
Answer:
\(\boxed {\boxed {\sf 3 \ meters}}\)
Explanation:
Work is the product of force and distance.
\(W=F*d\)
We know the force to lift the rock was 50 Newtons. The work was 150 Joules.
1 Joule is equal to 1 Newton meters. We can convert the units to make the problem simpler later. The work is also 150 Newton meters.\(W= 150 \ N*m \\F= 50 \ N\)
Substitute the values into the formula.
\(150 \ N*m= 50 \ N * d\)
We want to solve for distance, so we must isolate the variable. Divide both sides of the equation by 50 Newtons.
\(\frac{150 \ N*m}{50 \ N }=\frac{50 \ N * d}{50 \ N }\)
The Newtons will cancel out.
\(\frac{150 \ m }{50} =d \\3 \ m =d\)
The rock was lifted 3 meters.
What is the frequency of an electromagnetic wave having a wavelength of 300 000 km.
Answers
Answer:
below
Explanation:
300 000 km = 300 000 000 m
c = wl * f
3 x 10^8 = 300 000 000 m * f
1 hz = f
1. If the angle of the ramp were increased from 30˙ to 45˙, how would this change the weight of the box? Explain.
2.If the angle of the ramp were increased from 30˙ to 45˙, how would this change the weight of the box? Explain.
Answers
When the angle of the ramp increases, the weight of the box acting perpendicular to the ramp decreases.
Normal reaction of the boxThe normal reaction of the box is due to weight of the box acting perpendicular to the ramp.
Fn = Wcosθ
when the angle of the ramp = 30⁰Fn = Wcos(30)
Fn = 0.866W
when the angle of the ramp = 45⁰Fn = W x cos(45)
Fn = 0.7071W
Thus, when the angle of the ramp increases, the weight of the box acting perpendicular to the ramp decreases.
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What is the potential energy of a 2 kg bowling ball resting at the top of a 5 m high hill? Show all of your work and include the correct units to receive full credit.
Answers
Answer:
\(\boxed {\boxed {\sf 98 \ J}}\)
Explanation:
We are asked to find the potential energy of a bowling ball.
Potential energy is the energy an object possesses due to its position. It is calculated using the following formula.
\(E_p= mgh\)
In this formula, m is the mass, g is the acceleration due to gravity, and h is the height.
The bowling ball has a mass of 2 kilograms. The hill is 5 meters high. Assuming this situation is occurring on Earth, the acceleration due to gravity is 9.8 meters per second squared.
m= 2 kg g= 9.8 m/s²h= 5 mSubstitute the values into the formula.
\(E_p= (2 \ kg )(9.8 \ m/s^2)(5 \ m)\)
Multiply the numbers together.
\(E_p=19.6 \ kg*m/s^2(5 \ m)\)
\(E_p=98 \ kg*m^2/s^2\)
Convert the units. 1 kilogram meter squared per second squared is equal to 1 Joule. Our answer of 98 kg*m²/s² is equal to 98 Joules.
\(E_p= 98 \ J\)
The bowling ball has 98 Joules of potential energy.
Which is an example of the force of attraction between two objects that have mass?
Magnetism
Gravity
Solar energy
Electricity
Answers
The wavelength of a particular color of orange light is 650 nm. The frequency of this color is ____ sec-1 (1 nm = 10-9 m)
Answers
The frequency of the orange light is 4.6 x 10^14 sec^-1. To calculate the frequency, we can use the formula: frequency = speed of light / wavelength. The speed of light is approximately 3 x 10^8 m/s. However, we need to convert the wavelength from nm to m by multiplying it by 10^-9. So,
frequency = (3 x 10^8 m/s) / (650 x 10^-9 m)
frequency = 4.6 x 10^14 sec^-1
To find the frequency of the orange light with a wavelength of 650 nm, we will use the formula:
Frequency (f) = Speed of Light (c) / Wavelength (λ)
First, we need to convert the given wavelength from nanometers (nm) to meters (m) using the conversion factor 1 nm = 10^-9 m:
650 nm * (10^-9 m/nm) = 6.50 * 10^-7 m
Now, we will use the speed of light (c), which is approximately 3.00 * 10^8 m/s:
f = (3.00 * 10^8 m/s) / (6.50 * 10^-7 m)
After dividing, we get:
f ≈ 4.62 * 10^14 sec^-1
So, the frequency of this particular color of orange light is approximately 4.62 * 10^14 sec^-1.
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Work done by friction on a sliding mass A point mass m = 9 kg starts with speed to = 7 m/s at height h = 8 m on a slope as shown. The mass slides down the slope under the influence of gravity 9 .8 m/s2 and friction and at the bottom of the slope it has speed vf 5 m/s .What is the work W done by friction on the mass as it slides down the slope?
Answers
The work done by friction on the mass as it slides down the slope is 597.6 J.
To calculate the work done by friction on the mass as it slides down the slope, we first need to determine the change in kinetic energy of the mass and the work done by gravity.
The initial potential energy of the mass at height h is:
Ep = mgh = 9 kg × 9.8 m/s^2 × 8 m = 705.6 J
The final kinetic energy of the mass at the bottom of the slope is:
Ekf = (1/2)mvf^2 = (1/2) × 9 kg × (5 m/s)^2 = 112.5 J
The initial kinetic energy of the mass is:
Eki = (1/2)mv0^2 = (1/2) × 9 kg × (7 m/s)^2 = 220.5 J
Therefore, the change in kinetic energy of the mass is:
ΔEk = Ekf - Eki = 112.5 J - 220.5 J = -108 J
The negative sign indicates that the kinetic energy of the mass decreases as it slides down the slope.
The work done by gravity on the mass as it slides down the slope is equal to the change in potential energy:
Wg = -ΔEp = -705.6 J
The work done by friction is equal to the difference between the work done by gravity and the change in kinetic energy:
W = Wg - ΔEk = -705.6 J - (-108 J) = -597.6 J
The negative sign indicates that the work done by friction is in the opposite direction to the motion of the mass. Therefore, the work done by friction on the mass as it slides down the slope is 597.6 J.
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Electricity is converted into other forms of _________ such as heat, sound, or light.
Answers
Answer:
chemical i think
I hope this helped
Calculate the kinetic energy of a 10 kg object moving with a speed of 5 m/s.
Answers
Answer: the kinetic energy is equal to 125 Joules, or (1/2 * 10 kg) * 5 m/s2.
Explanation:
if a an object with a mass of 10 kg (m = 10 kg) is moving at a velocity of 5 meters per second (v = 5 m/s), the kinetic energy is equal to 125 Joules, or (1/2 * 10 kg) * 5 m/s2.
Answer:
The Kinetic energy of a 10Kg object moving with a speed of 5m/s is 125 Joules
Explanation:
Kinetic energy refers to the energy of a moving object. The formula for kinetic energy is given by
KE=(1/2)\(mv^{2}\).......(i)
, where, m⇒mass of object
v⇒velocity
and the unit is given by Joules.
Now, as we are given in the question,
mass, m=10kg
velocity, v= 5m/s
Substituting these values in the equation (i), we get,
KE=(1/2)x(10Kg)x(5m/s)^2,
we have,
KE=125 J
Therefore, the kinetic energy of a 10 kg object moving with a speed of 5m/s is 125 Joules.
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An electric field of 4.0 muV/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant?
The answer should be 0.40 A/s
Answers
The rate at which the current in the solenoid is changing at this instant is 4.4 A/s.
To determine the rate at which the current in the solenoid is changing, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) is equal to the negative rate of change of magnetic flux through a circuit. In this case, the solenoid acts as a circuit.
The induced electromotive force (emf) is given by:
emf = -dΦ/dt
Where:
emf is the induced electromotive force,
dΦ/dt is the rate of change of magnetic flux.
For a long solenoid, the magnetic flux (Φ) can be calculated as:
Φ = B * A
Where:
B is the magnetic field strength,
A is the area of the solenoid.
The magnetic field strength inside a solenoid is given by:
B = μ₀ * n * I
Where:
μ₀ is the permeability of free space (4π × 10^-7 T·m/A),
n is the number of turns per unit length (turns/m),
I is the current flowing through the solenoid.
Let's calculate the magnetic field strength (B) inside the solenoid:
B = μ₀ × n × I
= (4π × 10^-7 T·m/A) × (800 turns/m) × I
= (3.1831 × 10^-4) × I T
The area (A) of the solenoid can be calculated using the formula for the area of a circle:
A = π × r^2
Where:
r is the radius of the solenoid.
Let's calculate the area (A) of the solenoid:
A = π × r^2
= π × (0.03 m)^2
= 0.002827 m^2
Now, substitute the values of B and A into the formula for magnetic flux:
Φ = B × A
= (3.1831 × 10^-4) × I T × 0.002827 m^2
= 9.0 × 10^-7 × I Wb
Next, we differentiate the magnetic flux (Φ) with respect to time (t) to find the rate of change of magnetic flux:
dΦ/dt = d/dt (9.0 × 10^-7 × I)
= 9.0 × 10^-7 × dI/dt Wb/s
Finally, we can equate the rate of change of magnetic flux (dΦ/dt) to the induced electromotive force (emf) given in the problem statement:
emf = -dΦ/dt
= -9.0 × 10^-7 × dI/dt Wb/s
Given that the induced electromotive force (emf) is 4.0 μV/m = 4.0 × 10^-6 V/m, we can solve for the rate of change of current (dI/dt):
4.0 × 10^-6 V/m = -9.0 × 10^-7 × dI/dt
\(\frac{dI}{dt} = \frac{-(4.0) (10^-6 V/m)}{(9.0) (10^-7)} = -4.4 A/s\)
Therefore, the rate at which the current in the solenoid is changing at this instant is 4.4 A/s.
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Which list shows the correct order of processes that occur before and during ovulation?
egg released from ovary Right arrow. Hormones send signal Right arrow. Egg travels to fallopian tube
egg travels to fallopian tube Right arrow. Egg is released from ovary Right arrow. Hormones send signal
hormones send signal Right arrow. Egg travels to fallopian tube Right arrow. Egg released from ovary
hormones send signal Right arrow. Egg released from ovary Right arrow. Egg travels to fallopian tube
Answers
Hormones send signal → Egg released from ovary → Egg travels to fallopian tube.
Hormones send signal: The process of ovulation is triggered by hormonal signals. In the female reproductive system, the pituitary gland releases follicle-stimulating hormone (FSH) and luteinizing hormone (LH) in response to the signals from the hypothalamus. These hormones play a crucial role in the maturation of ovarian follicles and the release of an egg from the ovary.
Egg is released from the ovary: Once the hormonal signals are received, the dominant ovarian follicle (containing a developing egg) reaches maturity.
The surge in luteinizing hormone (LH) triggers the release of the egg from the ovary. This is known as ovulation. The released egg is then available for potential fertilization.
Egg travels to the fallopian tube: After ovulation, the released egg, also known as the ovum or oocyte, travels through the fallopian tube. The fallopian tubes, also called uterine tubes, are structures that connect the ovaries to the uterus.
The fallopian tubes have finger-like projections called fimbriae that help capture the released egg and guide it into the tube.
In summary, the correct order of processes before and during ovulation is as follows:
Hormones send signal
Egg is released from the ovary
Egg travels to the fallopian tube
These processes are essential for successful reproduction in females and are part of the menstrual cycle.
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Answer:
d
Explanation:
edge
A ball is swung in a horizontal circle at a constant speed. Each circle takes 0.85 seconds to complete and the rope is 0.40 m long. What is the centripetal acceleration?
Answers
Answer:
The centripetal acceleration will be "21.785 m/s²".
Explanation:
The given values are:
Time,
t = 0.85 seconds
Length of rope,
r = 0.40 m
Mass of ball,
m = 0.80 kg
As we know,
⇒ \(w=\frac{2 \pi}{t}\)
On substituting the values, we get
⇒ \(=\frac{2\times 3.14}{0.85}\)
⇒ \(= \frac{6.28}{0.85}\)
⇒ \(=7.38 \ rad/s^2\)
The centripetal acceleration will be:
⇒ \(a=r\times w^2\)
⇒ \(=0.40\times (7.38)^2\)
⇒ \(=0.40\times 54.46\)
⇒ \(=21.785 \ m/s^2\)