Answer:
laa a
Explanation:poque usairea ye aire tienfe luza preopia mkr
Answer:
Solar Panels
Explanation:
While catching an egg, the receiver "gives" with her hands and arms, making the
stopping time of the egg about seven times longer than if it were caught stiff-armed. By
what factor does the force encountered by the egg change?
Answer:
as the time has increased to 7 times so the force will decrease to 7 times as time of impact and force has inverse relation with each other
Explanation:
Work is best described as?
Answer:
Explanation:
In physics, work can be described as force multiplied by the displacement of the object (distance caused by the force acted on the object).
Work is a form of energy, therefore, it is measured in joules.
If Alex pushed on an object with 10N of force, and the object moved 2 meters, the work of Alex will be equal to:
W = Ft
W = 10N * 2m
W = 20 Joules
But, if we have John, that pushed on an object with 2N of force, but, since the object was way smaller, therefore it had way less inertia, the object moved a distance equal to 10 meters. Let's also calculate his work.
W = Ft
W = 2N * 10m
W = 20 Joules
And we got the same result.
Work can also be used to calculate power.
Power is equal to P = Work / time
It can also be written as P = delta Work / delta time
Power is measured in joules per second.
With power you can make the difference between someone that got a 2 kg object up in 2 second, and someone that got a 2 kg object up in 5 second.
The more powerful one would be the one who managed to make the same work in less time.
Hope it Helped!
Work is described as: the measure of energy transfer resulting from the application of force over a displacement.
What is Work?In the field of physics, work is most accurately defined as the outcome of multiplying the force exerted on an object by the distance the object is displaced in the same direction as the force.
This calculation serves to quantify the energy transferred to or from the object. For instance, if an individual applies a 50 Newton force to push a box across a 5-meter distance in the force's direction, the work done on the box would equal 250 Joules (50 N × 5 m).
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A 1.5 kg baseball is pitched at 38 m/s and is hit by the batter. It heads directly back at the pitcher at 27 m/s.
a) Find the impulse applied to the ball.
b) If the bat is in contact with the bat for 0.45 sec, how much force was applied.
Show all your work.
Answer:
The initial velocity of the ball is +38.0 m/s. The final velocity is -27.0 m/s.
momentum = mass x velocity
(mass x final velocity) – (mass x initial velocity)
(1.5)(-27) – (1.5)(38) = -97.5
The impulse applied to the ball is -97.5 kg m/s
impulse = force x time interval
force = impulse/time interval
-97.5/0.45 s = - 216.6
The force applied was 216.6 N.
A rocket burns fuel at a rate of 239 kg/s
and exhausts the gas at a relative speed of
6 km/s.
Find the thrust of the rocket.
Answer in units of MN.
The Thrust on the rocket is 1.434 MN.
To calculate the thrust of a rocket, we use the formula below
Thrust: This is the force that moves an aircraft through the air.
⇒Formula
T = M'×v.................... Equation 1⇒ Where:
T = Thrust of the rocketM' = Fuel ejection ratev = gas exhaust velocityFrom the question,
⇒ Given:
M' = 239 kg/sv = 60 km/s = 6000 m/s⇒ Substitute these values into equation 1
T = 239(6000)T = 1434000 NT = 1.434 MNHence, the Thrust on the rocket is 1.434 MN.
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Now consider four runners running around the track with the same constant tangential speed, with one runner in each lane of the track. A student in considering using the following equations to determine which runner has the greatest acceleration. Equation 1: V^2x=V^2xo+2Ax(X-X0) Equation 2: Ac=V^2/r Which equation should the student use, and why?answer choicesEquation 1, because the runners all have the same speed.Equation 1, because the different distances traveled by the runners in a complete lap around the track determine which runner has the greatest acceleration.Equation 2, because the acceleration term has already been isolated on the left-hand side of the equation.Equation 2, because the radius of the circular path traveled by a runner determines the acceleration of the runner.
The equation the student should use is equation 1, because the runners all have the same speed.
first option is the correct answer.
What is centripetal acceleration?The centripetal acceleration of an object is the radial or inward acceleration of an object moving a circular track.
There are several equations which can be used to determine linear acceleration of an object.
One of the equations is given in equation 2;
Vₓ² = V₀² + 2a ( x - x₀ )
where;
Vₓ is the final velocity of the objectV₀ is the initial velocity of the objecta is the acceleration of the objectx is the final displacement of the objectx₀ is the initial displacement of the objectwhen an object is moving at a constant velocity, the final velocity is equal to initial velocity, and the acceleration will become zero. So the equation two cannot be used since the runners are moving at a constant tangential speed.
The only equation that can be used to determine the maximum acceleration of the runner is the equation for centripetal acceleration.
a = v²/r
where;
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Need help please????????!!!!!!!!!!
Answer:
Your education back ground
when high voltages are present, a glow may be seen around sharp points, known as
When high voltages are present, a glow may be seen around sharp points, known as corona discharge.
This glow is caused by the ionization of the air molecules near the sharp point due to the electric field strength. The ionized air molecules emit light, creating a visible glow. The intensity and color of the glow depend on the voltage level and the gas composition of the surrounding environment.
Corona discharge is a phenomenon that occurs when high voltages are applied to a conductor, especially in the presence of a sharp point or a high electric field. It results in the ionization and excitation of the surrounding air molecules, creating a glowing or visible aura of light around the conductor. The ionized air can also produce a hissing or crackling sound. Corona discharge is often observed in high-voltage power lines, antennas, and other high-voltage equipment. It is important to note that corona discharge can cause power loss and interfere with the proper functioning of electrical systems, so efforts are made to minimize its occurrence in high-voltage applications.
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Which of the following is a limit of science? (2 points) a The technology or tools available to test scientific claims b The number of times an experiment can be repeated c The total number of scientists in a field, like physics or chemistry d The use of critical thinking and evidence to study phenomena
Answer: A- The technology or tools available to test scientific claims. I just took this test and passed.
Why is chlorine bonded by a single covalent bond, but Oxygen bonded by a double covalent bond?
Answer:
chlorine is a non-metal.
Explanation:
a chlorine atom has 7 electrons in its outer shell. chlorine is in group 7 of the periodic table. two chlorine atoms will each share one electron to get a full outer shell and form a stable cl2 molecule.
The total distance from a house to a school to is 9.5 km. A student travels all the way from his house to the school and back to his house again. The displacement during this journey is:
9.5 km
19 km
0
explain your answer
Answer:
0
Explanation:
Displacement is a vector from initial to final point. Because initial and final point are the same, so displacement is 0.
HURRY A spring with a spring constant of 350 N/m pulls a door closed. How much work is done as the spring pulls the door at a constant velocity from an 85.0-cam stretch to a 5.0-cm stretch?
In stretching or compressing the spring by a distance of x (in meters), one performs 1/2 (350 N/m) x² of work on the spring, or equivalently the spring performs -1/2 (350 N/m) x² of work on the door. This work is negative since the restoring force of the spring opposes the force used to stretch or compress the spring.
Then when the spring is allowed to relax, it performs 1/2 (350 N/m) x² of work to return it to equilibrium position. The force from the spring acts in the direction of the door's motion, so the work done is positive once more.
Now, the work done on the door …
• … to return it from 85.0 cm = 0.850 m to equilibrium is
1/2 (350 N/m) (0.850 m)² = 126.4375 J
• … to return it from 5.0 cm = 0.050 m to equilibrium is
1/2 (350 N/m) (0.050 m)² = 0.4375 J
• … to relax from 85.0 cm to 5.0 cm from equilibrium is
126.4375 J - 0.4375 J = 126 J
This is a continuation of Exercise 5 in Chapter 6. The golf fan was so impressed
with your answers to part 1 that your advice has been sought re the next stage in
the data analysis, namely using model selection to remove the redundancy in full
the model developed in part 1.
log(Y) = b0 + b1x1 + b2 x2 + b3x3 + b4 x4 + b5x5 + b6 x6 + b7 x7 + e (7. 10)
where
Y = PrizeMoney ; x 1 = Driving Accuracy ; x 2 = GIR ; x 3 = PuttingAverage ; x 4 =
BirdieConversion ; x 5 = SandSaves ; x 6 = Scrambling ; and x 7 = PuttsPerRound.
Interest centers on using variable selection to choose a subset of the predictors
to model the transformed version of Y. Throughout this question we shall
assume that model (7. 10) is a valid model for the data.
(a) Identify the optimal model or models based on 2
adj R , AIC, AICC, BIC from
the approach based on all possible subsets.
(b) Identify the optimal model or models based on AIC and BIC from the
approach based on backward selection.
(c) Identify the optimal model or models based on AIC and BIC from the
approach based on forward selection.
(d) Carefully explain why the models chosen in (a) & (c) are not the same while
those in (a) and (b) are the same.
(e) Recommend a final model. Give detailed reasons to support your choice.
(f) Interpret the regression coefficients in the final model. Is it necessary to be
cautious about taking these results to literally?
(a) To identify the optimal model or models based on adjusted R-squared (adj R2), AIC, AICC, and BIC from the approach based on all possible subsets, all possible combinations of predictors need to be evaluated. For each subset, the adjusted R-squared, AIC, AICC, and BIC values are calculated. The optimal models are those with the highest adj R2 and the lowest AIC, AICC, and BIC values.
(b) The optimal model or models based on AIC and BIC from the backward selection approach are determined by iteratively removing predictors that result in the lowest AIC and BIC values. The optimal models are those with the lowest AIC and BIC values.
(c) Similarly, in the forward selection approach, predictors are added iteratively to create models with the lowest AIC and BIC values. The optimal models are those with the lowest AIC and BIC values.
(d) The models chosen in (a) and (c) may not be the same because backward selection and forward selection follow different strategies for including or excluding predictors. However, the models chosen in (a) and (b) are the same because both approaches consider the same criteria (AIC and BIC) and aim to minimize these values.
(e) Recommending a final model requires considering the performance and interpretability of the models. The final model should strike a balance between simplicity and predictive power, choosing a subset of predictors that offer the best trade-off. Factors such as high adjusted R-squared, low AIC, AICC, and BIC values, and practical interpretability of the predictors should be considered.
(f) When interpreting the regression coefficients in the final model, it is essential to consider the context of the data and the assumptions of the model. Caution should be exercised as the coefficients represent the association between the predictors and the transformed outcome variable. The interpretation should be done in relation to the specific research question, taking into account potential limitations and the need for further validation or external confirmation.
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If we ignore lift and drag forces as the squid flies through the air, what is the maximum horizontal range that the squid can achieve before splashing down?
The speed is 42 m/s at which squid rejects the water.
The maximum horizontal range that squid can achieve is 1.25 m
What is a drag force?
Drag force is a force acting opposite to the relative motion of any object moving concerning a surrounding fluid. This exists between two fluid layers or between a fluid and a solid surface.
Here,
mass of the water, m1 = 3.0 kg
mass of the squid, m2 = 36 kg
initial speed, v2 = 3.5 m/s
(a)
According to the conservation of momentum:
m1*v1 = m2*v2
3 * v1 = 36 * 3.5
v1 = 42 m/s
It is the speed at which the squid rejects the water.
(b)
The maximum range:
R(max) = (v2) ^2 / g
where,
g=9.8 m/s^2 and launch angle is 45°
R(max) = 3.5^2 / 9.8
R(max) = 1.25 m
Hence,
The speed is 42 m/s at which squid rejects the water.
The maximum horizontal range that squid can achieve is 1.25 m
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Your question is incomplete, but most probably the full question was:
We’ve seen that squid can escape from predators by ejecting water. Some squid do this at the surface of the ocean, thus launching themselves into the air—a particularly effective escape strategy. Suppose a 36 kg squid (not including water) at rest at the surface of the water brings in and quickly ejects 3.0 kg of water to achieve a takeoff speed of 3.5 m/s; these are typical numbers.
a. At what speed does the squid eject the water?
b. If we ignore lift and drag forces as the squid flies through the air, what is the maximum horizontal range that the squid can achieve before splashing down?
under what conditions can an object be treated as a particle? (note that some quiz questions have multiple correct answer. the check box is square instead of round on these questions.) select one or more: a. object must be able to be treated as round b. forces on object must be concurrent c. object must not deform under the forces d. object must not change shape e. object must not be large f. object must not rotate
Forces on object must be concurrent. Object must not deform under the forces. Object must not change shape. Object must not be large. Object must not rotate.
What is force?Force is a physical quantity that represents the interaction between two objects. Force can cause an object to accelerate or change its velocity. It can also cause a change in an object's shape or orientation. There are several types of force, such as gravitational force, electromagnetic force, and nuclear force.
An object can be treated as a particle under the following conditions:
Forces on object must be concurrent. Object must not deform under the forces. Object must not change shape. Object must not be large. Object must not rotate.
It's important to note that the concept of treating an object as a particle is a simplifying assumption used in some branches of physics, such as mechanics, and is only valid under certain conditions.
When an object is treated as a particle, it is assumed to have no internal structure, and that all forces acting on it act at a single point. The object is also assumed to be small enough that its deformation or shape change under forces can be ignored. Additionally, it is also assumed that the object does not rotate.
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A pinball bangs against a bumper giving the ball a speed of 42cm/s if the ball has a mass of 50.0g what is the ball’s kinetic energy in joules
Explanation:
Given:-mass=50g
velocity=42cm/s
To find:-Kinetic energy
Solution:-As we know that
\({\boxed{\sf kinetic\:energy={\dfrac {1}{2}}mv^2}}\)
Substitute the values\({:}\longrightarrow\)\(\sf k.v={\dfrac {1}{{\cancel{2}}}}\times 50\times {\cancel{42}}^2 \)
\({:}\longrightarrow\)\(\sf k.v=50\times 21^2 \)
\({:}\longrightarrow\)\(\sf k.v=50×441 \)
\({:}\longrightarrow\)\(\sf k.v=22050MJ \)
1Joule=1000milijoules22050MJ=\({\dfrac {22050}{1000}}=22.05J\)=22J(Approximately)\(\therefore\)\({\underline{\boxed{\bf Kinetic\:energy=22Joule}}}\)
Can you tell me what a substance is
Answer:
Explanation:
a particular kind of matter with uniform properties.
Answer:
a particular kind of matter with uniform properties or the real physical matter of which a person or thing consists and which has a tangible, solid presence.
Explanation:
Why does a traveller's bag have wheels
Answer:
To make carrying the loads easier
Answer:
It's convenient and easy to rove a traveller's bag when it has wheels. You could easily drag the bag without hesitation instead of lifting it or pushing it heavily.
An axially loaded short column has length of 3.5m carries factored load of 1600KN. Concrete fc'=28MPA and Fy=420 MPA. Maximum aggregate size is 19mm. Calculate the suitable dimensions for tied and spiral columns.qr 1. Calculate • Required loads • Stresses • Gross area • Area of steel • Design satisfies risk assessment against use Appropriate reinforcement SELECTION • All relevant checks to make design safe
The suitable dimensions for tied and spiral columns of Required loads, Stresses, Gross area, Area of steel are 1142.86 kN, 12.6 MPa, 90.89 m².
The required loads can be determined by dividing the factored load by the appropriate load factor. For this example, let's assume a load factor of 1.4. Required loads = Factored load / Load factor
= 1600 kN / 1.4
= 1142.86 kN
Determine the allowable stresses: a concrete compressive strength of fc' = 28 MPa, the allowable compressive stress (fa) can be calculated using the formula:
= 0.45 * 28 MPa
= 12.6 MPa
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what is the wavelength in micrometers of light with a frequency of 3.2 × 1012 hz?
The wavelength of light with a frequency of 3.2 × 10¹² Hz is 93.75 μm
The wavelength in micrometers of light with a frequency of 3.2 × 10¹² Hz
can be calculated by using the formula:
c = λν
where c is the speed of light,
λ is the wavelength, and
ν is the frequency of light.
Therefore,
λ = c / νλ = c / ν = (3 × 10⁸ m/s) / (3.2 × 10¹² Hz) = 9.375 × 10⁻⁵ m
which can be expressed in micrometers as:
λ = (9.375 × 10⁻⁵ m) × (10⁶ μm/m) = 93.75 μm
Wavelength is the distance between two consecutive points on a wave that are in phase. It is the distance between the peaks of a wave or the distance between the troughs of a wave.
The wavelength is determined by the velocity of the wave and the frequency of the wave.
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what is the first step in creating a successful long-term goal
First consider what you want to achieve, and then commit to it. Set SMART (specific, measureable, attainable, relevant and time-bound) goals that motivate you and write them down to make them feel tangible. Then plan the steps you must take to realize your goal, and cross off each one as you work through them.
The first step in creating a successful long-term goal is to define what you want to achieve.
This involves setting a clear and specific objective that you can work towards over an extended period of time. To define your goal, start by identifying your passions, interests, and values. For example, if you are passionate about environmental conservation, your long-term goal might be to start your own nonprofit organization focused on protecting endangered species.
Once you have a general idea of what you want to achieve, it's important to make your goal SMART: Specific, Measurable, Achievable, Relevant, and Time-bound. This means breaking down your goal into smaller, actionable steps that are realistic and can be measured or evaluated.
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20 pts) NaLi molecule (sec. 5.3, p.75) has a built-in polarization. The inter-atomic distance d=3.0A˚. If one would apply an electric field along the molecular axis to cancel the polarization, in which direction and what magnitude should the field be? Also determine the filed (direction and magnitude) to double the polarization. Use the energy levels given in the textbook (sec. 5.3), and Vss σ given in (6.6), p.95. Use V/cm for the unit of the electric field. <2∣H∣1>VssσVppσ≡∫ψ2 s(r−r2)∗Hψ2 s(r−r1)d3r=−8π2md2ℏ2,=+83π2md2ℏ2,Vspσ=+2πmd2ℏ2Vppπ=−8π2md2ℏ2
To cancel the polarization of a NaLi molecule, an electric field of magnitude 5.33 V/Å needs to be applied along the molecular axis in the direction opposite to the polarization.
To double the polarization of a NaLi molecule, an electric field of magnitude 10.66 V/Å needs to be applied along the molecular axis in the direction of the polarization.
The polarization of a NaLi molecule is due to the difference in electronegativity between sodium and lithium. Sodium is more electropositive than lithium, which means that it has a stronger affinity for electrons.
This means that the electrons in the NaLi molecule are more likely to be found closer to the sodium atom than the lithium atom.
The electric field will exert a force on the electrons in the NaLi molecule, trying to pull them away from the sodium atom and towards the lithium atom. If the electric field is strong enough, it will be able to cancel the polarization of the molecule.
The magnitude of the electric field needed to cancel the polarization of a NaLi molecule can be calculated using the following formula:
E = 2qd / e
where:
E is the magnitude of the electric field
q is the charge of an electron
d is the inter-atomic distance
e is the permittivity of free space
In this case, the magnitude of the electric field needed to cancel the polarization of a NaLi molecule is:
E = 2 * (1.602 * 10^-19 C) * (3.0 * 10^-10 m) / (8.854 * 10^-12 C^2 / N m^2) = 5.33 V/Å
To double the polarization of a NaLi molecule, the electric field would need to be twice as strong. This means that the magnitude of the electric field would need to be 10.66 V/Å.
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Light travels (fastest, slowest) in media with a lower index
of refraction value.
Fastest
Light travels fastest in media which are least optically dense. The index of refraction value provides a relative measure of the optical density of a material. The higher the index of refraction value, the more optically dense a material is and the slower that light will travel in that material.
a wheel has a constant angular acceleration of 7.0 rad/s2 starting frm rest it turns through 400 rad
It takes approximately 10.69 seconds for the wheel to turn through 400 rad.
To find the time it takes for the wheel to turn through 400 rad, we can use the kinematic equation for angular displacement:
θ = ω₀t + (1/2)αt²
where θ is the angular displacement, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
Given:
Angular acceleration (α) = 7.0 rad/s²
Angular displacement (θ) = 400 rad
Initial angular velocity (ω₀) = 0 rad/s (starting from rest)
Rearranging the equation to solve for time (t):
θ = (1/2)αt²
400 rad = (1/2)(7.0 rad/s²)t²
800 rad = 7.0 rad/s²t²
t² = 800 rad / (7.0 rad/s²)
t² ≈ 114.29 s²
t ≈ √(114.29) s
t ≈ 10.69 s
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An object of mass 20kg was dropped from the top of a building of height 200m
Calculate:
a)what time does it take the object to fall freely the a distance of 120m
b)The velocity of the object at the distance
c)With what velocity will the object strike the ground?(g=10m/s²)
The time it takes the object to fall freely at a distance of 120m is 7.75 sec.
Velocity is the directional pace of an item in motion as an indication of its rate of exchange in the role as determined from a selected frame of reference and as measured by way of a selected standard of time.
Calculation:-
mass = 20 kg
height = 200 m
new height = 120
S = ut +1/2at²
120 = 0 + 0.5× 10 t²
t² = 120/5
= 60
= 7.75 sec
Average velocity is calculated by means of dividing your displacement (a vector pointing out of your initial role in your final position) through the entire time; the average pace is calculated by way of dividing the overall distance you traveled by means of the total time.
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A car accelerates if it:
Speeds up
Slows down
Goes around a curve
Both A and B
A, B, and C
Answer:
A because when you accelerate you move even faster
Why must the intersection of the 3 lines be the
Centre of gravity?
The intersection of the three lines in the triangle is the point where the three lines intersect. This point is the centroid or center of gravity of the triangle.
What is the Centre of gravity?The centroid is the point of balance of the triangle where all three medians meet. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.
The medians of a triangle divide it into six smaller triangles of equal area. The centroid is the point where these six smaller triangles balance out each other's weight.
Therefore, Since the medians divide each other in a 2:1 ratio, the centroid is located 2/3 of the distance from each vertex along the median. Hence, the intersection of the three lines at this point gives us the center of gravity of the triangle.
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Calculate the energy transfered when 3 of copper is heated from 20°C to 220°C
Answer:
Q = 231.6 J
Explanation:
Given that,
Mass, m = 3 g
The temperature rises from 20°C to 220°C.
We know that, the specific heat of copper is, c = 0.386 J/g K
We know that the energy transferred in heating of copper is given by :
\(Q=mc\Delta T\\\\Q=3\times 0.386\times (220-20)\\\\Q=231.6\ J\)
So, the required energy is equal to 231.6 J.
The arrows in the image below represent the processes that occur as water goes through phase changes. How is water different after changing from a gas to a liquid through process 2?
A. The water is warmer. B. The water particles move slower. C. The water particles are spread farther apart. D. The water takes up more space.
After changing from a gas to a liquid through process 2, the water particles are different in several ways. The correct answer is B. The water particles move slower. the correct difference in water after changing from a gas to a liquid through process 2 is that the water particles move slower.
During process 2, which represents the condensation of water vapor, the gas particles lose energy and transition into a liquid state. This loss of energy causes the water particles to slow down their movement and come closer together, forming liquid water molecules. In the gas phase, water molecules have high kinetic energy, moving rapidly and freely. However, as the gas cools down during condensation, the kinetic energy decreases, resulting in slower particle movement. The particles become more constrained by intermolecular forces, allowing them to adhere to one another and form liquid droplets. While the water particles do come closer together during condensation, they do not spread farther apart as mentioned in option C. Additionally, the water does not take up more space (option D), as the transition from a gas to a liquid involves a decrease in volume.
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W=225 J
P=25 W
t=?
what's T
Answer:
T is 9s.
Explanation:
In power formula Power (P) = work done(W)/time (t) . Make time(T) the subject.
Therefore time is work done÷ power
Time (T) = 225J÷25W
Time(T) = 9s
Therefore T is 9s.
II. Practice calculations:
1. A current of 2.24A flows in a straight wire oriented along the x-axis so the current flows to the left. What is the
magnitude and direction of the magnetic field created by the wire at a point that is 0.022m above the wire? What is the
magnitude of the field at a point twice as far above the wire as point X? 10 times as far below the wire?
Hi there!
For a straight wire, we can use Ampère's Law to find its magnetic field at various distances from the wire.
Using the equation:
\(\oint B\cdot dl = B \cdot l = \mu_0 i\)
B = Magnetic field strength (T)
l = length of path of integration (m)
μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)
i = Enclosed current (2.24 A)
This is a dot-product, so the cosine of the angle between the magnetic field and the path of integration is considered. However, since we are always tangential to the magnetic field, cos(0) = 1. We can simplify to B * l.
The length of the path of integration is equivalent to the circumference of a circle produced with a radius 'r' as a straight, long wire creates circular magnetic fields around the wire.
Therefore:
\(C = 2\pi r\\\\B \cdot 2\pi r = \mu_0 i\)
Solve for 'B'.
\(B = \frac{\mu_0i}{2\pi r}\)
1.
Plug in the given values and solve for the strength of the magnetic field at r = 0.022m.
\(B = \frac{(4\pi \times 10^{-7})(2.24)}{2\pi (0.022)} = \boxed{20.364 \mu T}\)
Using magnetic hand rules, a left-flowing (-x axis) current will result in a magnetic field of this strength INTO THE PAGE (or +y-axis if we assign the +/- z-axis to be up/down respectively) above the wire.
2.
Since B ∝ 1/R, if we double 'R', B will be halved.
Therefore:
\(B_{2R} = \frac{B_R}{2} = \frac{20.364 \mu T}{2} = \boxed{10.182 \mu T}\)
3.
The same logic applies. If we increase 'R' by 10x, B will decrease by 10x.
\(B_{10R} = \frac{B_R}{10} = \frac{20.364\mu T}{10} = \boxed{2.0364 \mu T}\)
However, since this point is BELOW the wire, the direction of the magnetic field differs. Using hand rules, the field would point OUT OF THE PAGE, or to the -y-axis.