A hockey player is standing on his skates on a frozen pond, if he accelerates uniformly at 0.22 m/s2, the player will catch his opponent in 19.49 seconds.
Uniform Motion
The object's uniform motion should follow the following rules as provided
vt = vo + at
vt² = vo² + 2a . s
s = vo*t + 1/2*a*t²
Here vt is seen as the final velocity, vo = initial velocity
a= acceleration t= time and s= displacemnt
according to the question,
v = 2
t= 1.4
vo= 0 m/s
a = 0.22 m/s²
The distance between the players is seen as
Vt= 2x 1.4 = 2.8 m
The player will thus catch his opponent with the same distance. This means,
Sopponent = Splayer
so + vt = vo*t + 1/2 at²
⇒ 2.8 + 2.t = 0 . t + 1/2 . 0.22 . t²
⇒ 0.11t² - 2t - 2.8 = 0
⇒ t = 19.49 s
on solving the above quadratic equation, we calculate the possible root as 19.49 seconds.
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Guys fr i don't understand physics
if it takes 10 seconds to drive around 450 cm.
Using your mathematical model, calculate the distance your car would travel at 15 seconds.
Answer:
675
Explanation:
10 seconds = 450 cm
1 second = 450 ÷ 10 cm
15 seconds = 450 ÷ 10 × 15 cm
" = 45 × 15 cm
" = 675 cm
Thus , 675 is the answer
11. the square of the speed of an object undergoing a uniform acceleration a is some function of a and the displacement s, according to the expression given by
v^2 = k am sn,
where k is a dimensionless constant.
we have to tell the whether it is dimensional or dimensionless
v = m/sec dimesions
a = m/sec^2 dimesion, m = m
v^2 = m^2 / sec^2 = k m/sec^2 * m
k = dimesionless constant.
Dimension is a measurable extent, such as the three principal dimensions of an object of width, height, and depthdimension is of many types radial, angular, linear etc.Reference Dimensions is a Dimension without a tolerance, used for information purposes only. A reference is a repeat of a given dimension or established from other values one dimension is practically not found.To know more about Dimension visit : https://brainly.com/question/1374629
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objects that are flying around (like sand in a dust storm) can become electrically charged. how much charge these objects accumulate varies, but a reasonable scale is pc (10-12 coulombs). if a grain of sand has a net charge of 59pc, approximately how many electrons has it lost?
The number of electrons lost is 3.69 * 10^8 electrons
What is the number of electrons lost?We know that charge that is carried by an electron has the magnitude of 1.6 * 10^-19C. In this case we have been asked to obtain the number of electrons that could be lost in the process and we have the charge as 59pc.
Knowing that;
Q = ne
Q = magnitude of charge
n = number of electrons
e = magnitude of charge on an electron
n = Q/e
n = 59 * 10^-12/1.6 * 10^-19C
n = 3.69 * 10^8 electrons
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A driver starts his parked car and within 5 hr reaches a speed of 60 km/h, as he travels east. what is his acceleration?
Answer:
change in speed) / (time for the change)
and the direction of the change.
Acceleration = (60 - 0) km per hour / 5 sec = 12 km per hour per second, east.
I hear teachers all over the country complaining about that ugly unit.
It has to be changed to a more familiar unit of acceleration.
(12 km/hour) x (1 hour/3600sec) = 12,000/3600 = 3-1/3 meter/sec.
His acceleration is 3-1/3 meters per second² .
Explanation:
a
Answer:
u=0
v=60 km/ hr
60 \times 1000 \\ 60 \times 60 = 1800
t =5
t = 5 \times3600 = 18000
a= ?
a = v - u \div t
= 1800 - 0 \div 18000 \\
1m/s^2\: ans
An object is dropped from the top of a building and hits the ground 3 seconds after it is released. what is the approximate speed of the object at the instant it hits the ground?
Once the object is dropped ,The only force acting on it is gravity.so acceleration due to gravity is 9.8 m/[tex]s^{2}[/tex].
Given,
Initial velocity = u = 0
Time taken = t = 0
Acceleration = g = 9.8 m/[tex]s^{2}[/tex]
Using [tex]3^{rd}[/tex] equation of motion ,
v = u + at
v =( 0 )+ (9.8) *(3)
v = 29.4
v≈ 30 m/s
So, the speed of object is 30 m/s.
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you quickly need a 133-ω resistance value but only have a collection of 100-ω resistors. what can you do?
The series combination will give you the resistance of 200ohm when two 100ohm resistances are connected.
What is resistance?Resistance is a device used to restrict the flow of the current. By using ohm's law the resistance is the ratio of the potential difference applied across the circuit and the current flowing through the circuit.
Given that you quickly need a 133-ω resistance value but only have a collection of 100-ω resistors.
For this case use the series combination of the resistances in which the resistances are connected in series by doing so the effect of resistance is increased.
R = R1 + R2
If you have two 100 ohm resistances connect them in the series.
R = R1 + R2
R = 100 + 100
R =200 ohm
Therefore, the series combination will give you a resistance of 200ohm when two 100ohm resistances are connected.
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When randomly arranged low energy protons enter the magnetic field they become static and ______________ with the main magnetic field and net magnetization.
When randomly arranged low-energy protons enter the magnetic field they become static and parallel with the main magnetic field and net magnetization.
What is net magnetization?The magnetic moments of each individual hydrogen atom are added to create the net magnetization vector in MRI. Individual magnetic moments are arbitrarily oriented when there is no external magnetic field, and because they are in opposition, the net magnetization vector is thought to be zero.
How magnetization m is connected with the magnetic field?The intensity of magnetization, or just magnetization, is the term used to describe the magnetic dipole moment per unit volume of a substance (M). The relationship between the applied magnetic field (H) and the material's internal magnetic flux density or magnetic induction (B) is linear.
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the head of a nail is 0.39 cm0.39 cm in diameter. you hit it with a hammer with a force of 27 n.27 n. what is the pressure pheadphead on the head of the nail?
The nail head has a zero.39 cm diameter. You strike it with a hammer that has 27 N of force. at the nail head, there might be a stress head of 31100716.5 Pa.
Pressure P = Force(F) / Area(A)
On nail head = P = [tex]\frac{F}{\pi r^{2}}[/tex]
[tex]= \frac{f}{\pi (\frac{d}{2} )^{2} }[/tex]
[tex]= \frac{4F}{\pi d^{2} }[/tex]
[tex]P = \frac{25*4}{3.14*0.0032^{2} }[/tex]
= 3110071.65 Pa
Pressure at the end of the nail P = [tex]\frac{F}{A}[/tex]
[tex]P = \frac{25*4}{3.14*0.00032^{2} }[/tex]
P = 31100716.5 Pa
pressure is the ratio of the force applied perpendicularly to an object's surface to its location. Its abbreviation is "p" or "P."
A fluid column whose weight is similar to the fluid's strain is represented with the aid of the strain head.
The elevation head represents the gravitational capacity energy resulting from elevation, even as the pressure head reflects the energy because of pore fluid stress
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light strikes a 5.0-cm thick sheet of glass at an angle of incidence in air of 50°. the sheet has parallel faces and the glass has an index of refraction 1.50. a. what is the angle of refraction in the glass? b. after traveling through the glass the light re-emerges into the air. what is the final angle of refraction in air? c. as it leaves the glass, by what distance is the path of the ray is displaced from what it was before entering the glass?
The angle of refraction in the glass is 30°.
Calculationi= 50°
u= 1.50
u1sini=u2sinr
⇒sinr =[tex]\frac{sin 50}{1.5\\}[/tex]
=0.50=1/2
so angle r = [tex]sin^{-1}[/tex](0.5) =30°
Then we have to calculate r final.
[tex]u_{glass}[/tex]sini= [tex]u_{air}[/tex] sinr
⇒ r = [tex]sin^{-1}[/tex] (1.5 x [tex]\frac{\sqrt{3} }{2}[/tex])
[tex]sin^{-1}[/tex](1.29) = 0.0225
Then the displacement can be calculated as follows:
T= thickness = 5cm
s= t (1- 1/u)
s= 2cm
Thus, all the values have been found out.
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list the experimental evidence that strongly suggested that light does not act like a wave during the photoelectric effect.
Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light
Publicized early in the debate about whether light was composed of particles or waves, a wave-particle dual nature soon was found to be characteristic of electrons as well.
The evidence for the description of light as waves was well established at the turn of the century when the photoelectric effect introduced firm evidence of a particle nature as well.
On the other hand, the particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer established the wave nature of the electron.
The details of the photoelectric effect were in direct contradiction to the expectations of very well developed classical physics.
The explanation marked one of the major steps toward quantum theory.
The remarkable aspects of the photoelectric effect when it was first observed were:
1. The electrons were emitted immediately - no time lag!
2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy!
3. Red light will not cause the ejection of electrons, no matter what the intensity!
4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths.
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doppler radar uses energy to measure the velocity and direction of movement of particles of rain or hail within a cloud.
Doppler radar measures the speed and direction of hail or raindrop movement within a cloud using microwave energy.
What is a doppler radar?A Doppler radar is a specialized radar that can gather velocity information on distant objects using the Doppler effect. This is done by directing a microwave signal at a target and observing how the target's movement changes the frequency of the signal that is reflected back. The difference between a wave's observed frequency and its emitted frequency when the observer is moving with respect to the wave source is known as the Doppler effect, sometimes known as the Doppler shift, and named after the Austrian scientist Christian Doppler who originally proposed it in 1842. The radial component of a target's velocity in relation to the radar can be directly and extremely accurately measured using this variation. It frequently happens while a vehicle with sirens moves toward, past, and away from a target.
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Which of the following correctly describes the axes and units of
a position-time graph?
A position-time graph shows how far an object has traveled from its starting position at any given time since it started moving.
The graph on which the immediate function x of a particle is plotted at the y-axis and the time t on the x-axis is called the position-time graph.
The distinction between them is that the velocity-time graph famous the speed of an item and whether it's miles slowing down or dashing up, whilst the position-time graph describes the motion of an item over a period of time.
Position-time graph and displacement-time graph is same. but each are different from distance-time graph. role-time graph and displacement-time graph may be bad. Distance-time graph can by no means be negative.
The shapes of the position-time graph for these basic varieties of motion - consistent pace movement and multiplied movement i.e., converting speed - monitor an vital precept. The precept is that the slope of the road on a position-time graph well-known shows beneficial statistics about the speed of the item.
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If a bird catches its prey from a height which is initially at rest them the momentum is conserved for
The momentum of both the engaged animals—a bird and its prey—is conserved.
What does linear momentum conservation mean?
If there is no external force acting on the colliding objects, the total momentum before and after the collision will be the same, according to the conservation of momentum principle.
Initial momentum is the same as final momentum.
As a result, both the engaged animals—a bird and its prey—keep their momentum.
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Make the following prefix conversions.
600,000 cm = Km
0.06
60
6
0.6
Answer: 6 km
works on odyseyware
The answer would be is 6 km
a student says " A running squirrel has a speed of -7 m/s . what is wrong with this statement.
I will give brainlist
During each cycle of operation, a refrigerator absorbs 230 j of heat from the freezer and expels 356 j of heat to the room. how much work input is required in each cycle?
126 J work input is required in each cycle .
Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
Mathematically, the above statement is expressed as follows:
W = (F cos θ) d = F. d
Where,
W is the work done by the force.
F is the force, d is the displacement caused by force
θ is the angle between the force vector and the displacement vector
The dimension of work is the same as that of energy and is given as, [ML2T–2].
Given,
refrigerator absorbs 230 J of heat from the freezer
expels 356 J of heat to the room
work input is required in each cycle = 356 - 230
= 126 J.
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why did scientists using classical, newtonian physics have difficulty explaining the photoelectric effect
The correct answer is :
According to classical electrodynamics, light energy is a wave that is absorbed by atoms in a manner similar to how an object absorbs radiant heat. So, the atoms of a metal would absorb more energy the brighter the light was. It would be feasible for an electron in a metal to break free from its atoms if it received enough energy from the incoming wave. The more energy absorbed, the more energetic the metal's released electrons would be. Additionally, no electrons could conceivably be ejected until each atom had enough light energy. Light intensity was far more important than light frequency.
In many respects, the photo-electric effect contradicted this strategy:
If the light was below a specific frequency, no matter how bright it was, no electrons were released. Increased light intensity increased the number of electrons that were released, but not their energy, if the light was above this frequency.Regardless of how weak the light was, electrons were nearly immediately emitted from the metal. Even though the intensity of the light was reduced, an increase in its frequency led to more energising electrons leaving the metal.To learn more about photo-electric effect refer the link:
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a 1.5\,\text {kg}1.5kg1, point, 5, start text, k, g, end text mass attached to an ideal spring oscillates horizontally with an amplitude of 0.50\,\text m0.50m0, point, 50, start text, m, end text. the spring constant is 85\,\dfrac{\text n}{\text m}85 m n 85, start fraction, start text, n, end text, divided by, start text, m, end text, end fraction.
spring P.E = 1/2 kx^2
= 1/2 * 250 x 0.25 = 31.25 N
where k= spring constant = 250 N/m
x= Compression = 0.250
By Applying conservation of energy
K.Ei+ P.Ei =K.Ef+ P.Ef
0+ 31.25 = 0+ m(9-8)(0.5)
4.9m =31.25
m= 6.377 kg
m- 6.4kg
law of conservation of energy sates the amount of energy you start with is the amount of energy you end with; the amount of energy always stays the same though its form may changePotential energy is the energy something stores because of position or structureKinetic energy is the energy something has because it is movingTo know more about conservation of energy visit : https://brainly.com/question/2137260
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Answer: 1.2 Hz
Explanation:
Khan Academy
A light-rail train going from one station to the next on a straight section of track accelerates from rest at 1.1 m/s2 for 20 s. it then proceeds at constant speed for 1100 m before slowing down at 2.2 m/s2 until it stops at the station. what is the distance between the stations?
The distance between the stations is 1320 m
How to determine the distance travelled in the first 20 sWe'll begin by calculating the distance travelled by the train in the first 20 s. This can be obtained as follow:
Initial velocity (u) = 0 m/sAcceleration (a) = 1.1 m/s²Time (t) = 20 sDistance (s) =?s = ut + ½at²
s = (0 × 20) + (½ × 1.1 × 20²)
s = 0 + 220
s = 220 m
How to determine the distance between the stationsThe distance between the stations can be obtained as illustrated below:
Distance in the 1st 20 s = 220 mDistance in the remaining journey = 1100 mTotal distance =?Total distance = 220 + 110
Total distance = 1320
Thus, the distance between both stations is 1320 m
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what is a set of particles or interacting components considered to be a distinct physical entity for the purpose of study.
a system is a collection of particles or interacting parts that is regarded as a unique physical entity for the purposes of study.
What is a physical entity?It is an entity that has a physical existence. An entity is something that exists in itself, real or potential, concrete or abstract, physical or not. It does not have to be of material existence. In particular, legal abstractions and fictions are generally considered entities. Also, in general, an entity is not considered animate. The word entitative is the adjective form of the nominal entity. Something entity is considered for itself. In philosophy, ontology consists in recognizing entities. The words ontic and entity derive from the present participles of ancient Greek and Latin, respectively, meaning being.
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Find the maximum height ymax reached by the rocket. ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .
Answer:
11,907 m is the maximum height ymax reached by the rocket.
Explanation:
The equations which relate displacement, velocity, acceleration and time are known as Equation of Kinematics. In this problem we use second and third equation of kinematics solve,
s = vit+1/2at2
V2f − V2i=2as
It is important to note from the information provided in the question
Acceleration in the first phase a1=49.0m/s2
Time for acceleration t=9.00s
Acceleration in the second phase a2=−9.8 ms-2
Height reached in first phase
y1=vit+1/2a1t2
y1 =0ms-1 × 9.00s + 12×49.0 ms-2 × (9.00s)2
=1984.5m
velocity at the end of first phase
v1=49.0 ms-2 × 9.00s
=441m/s
Now height reached in the second phase
V2f − V21 = 2a2y2
At maximum height final velocity is zero.
=02−(441.0m/s)2
=2(−9.80 ms-2) y2
y2=(0-(441.0 ms-2))/(2×(-9.80ms-2))
=9922.5m
So, the maximum height ymax reached by the rocket
ymax = y1+y2
ymax =1984.5m+9922.5m
=11907m
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two vectors, one with a magnitude of 14 units and one with a magnitude of 5 units, are both pointing east. what is the resultant of these two vectors?
The resultant of these two vectors is 19 units of two vectors, one with a magnitude of 14 units and one with a magnitude of 5 units, are both pointing east.
Explanation
As we know R = A + B
where is R resultant A and B are vectors is possible only if the both the vectors are in the same direction.
Therefore, R = 14 + 5
19 units
What is resultant force?A resultant force is the single force and corresponding torque that are created when a system of forces and torques acting on a rigid body is added together using vectors in physics and engineering. A consequent force, also known as a resultant force-torque, is one that acts on a rigid body in the same way as the initial system of forces.
Through computational analysis or (in the case of sufficiently simple systems) a free body diagram, the resultant force on a body is calculated and visualized.
The resultant force's location of application defines the torque it produces. Some people use the term resultant force-torque to describe the forces and torques acting on a rigid body; the word resultant force should be understood to include both.
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An accelerometer is made with a crystal of natural frequency 20 khz. the damping ratio of the accelerometer is found to be 0.71. determine the upper cutoff frequency of the accelerometer for 1 accuracy.
The upper cutoff accelerometer is made with a crystal of natural frequency of the accelerometer is 7.334 KHz.
What is accelerometer?An accelerometer is a tool that precisely measures acceleration. Proper acceleration is the acceleration of a body in its own instantaneous rest frame, as opposed to coordinate acceleration, which is acceleration in a fixed coordinate system.
Accelerometers are devices that measure the acceleration or vibration of a structure. They have a transducer that converts mechanical force caused by vibration or a change in motion into an electrical current by using the piezoelectric effect.
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A ______ focal length lens makes the background and foreground appear closer together.
Short focal length lens makes the background and foreground appear closer together.
What is a short focal length made lens?Short focal length lenses are sometimes known as wide-angle or wide-field lenses, which accurately defines their key characteristic—they view a larger angle of a scene than is typical.
When your eyes are fixed in one place and you look at a scene, a lens with a typical focal length captures what you see.
Are shorter focal lengths preferable?The angle of view is narrower, and the magnification is higher the longer the focal length.
What are short lenses used for?A shorter focal length results in a wider angle of view and a lower magnification.
Because they provide a broad field of view, short focal length lenses are frequently utilized in architectural, documentary, and landscape photography. These telephoto lenses enable
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a boat is stationary at 12\, \text{meters}12meters12, start text, m, e, t, e, r, s, end text away from a dock. the boat then begins to move toward the dock with an acceleration of 5.0\, \dfrac{\text{m}}{\text{s}^2}5.0 s 2 m 5, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. how long will it take the boat to reach the dock?
The time taken for the boat to reach the dock is 2.19 s
Data obtained from the questionFrom the question given above, the following data were obtained:
Initial velocity (u) = 0 m/sDistance (s) = 12 mAcceleration (a) = 5 m/s² Time (t) = ?How to determine the timeThe time taken for the boat to reach the dock can be obtained as illustrated below:
s = ut + ½at²
12 = (0 × t) + (½ × 5 × t²)
12 = 0 + 2.5t²
12 = 2.5t²
Divide both side by 2.5
t² = 12 / 2.5
Take the square root of both side
t = √(12 / 2.5)
t = 2.19 s
Thus, the time taken is 2.19 s
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If liquid water at 30 c is flowing in a pipe and the pressure drops to the vapor pressure, what happens in the water?
If liquid water at 30 degrees Celsius is flowing in a pipe and the pressure drops to the vapor pressure, the water starts to boil
In any liquid kept inside an evacuated chamber, the molecules of the liquid which have high kinetic energy enough to allow them to escape the surface of the liquid, turn into vapor. These molecules in the vapor phase start exerting pressure on the surface of the liquid and this pressure exerted by the vapor of same liquid is termed as the vapor pressure.The vapor pressure is very important parameter to decide the boiling point of the liquid. When the vapor pressure becomes equal to the pressure exerted by the surrounding atmosphere on the liquid, the liquid starts to boil irrespective of the temperature. The temperature at which vapor pressure becomes equal to the surrounding atmospheric pressure is known as the boiling point of the liquidIn the given problem, the liquid water which is flowing inside the pipe observes the pressure drop to vapor pressure. As soon as the pressure of liquid water drops to vapor pressure the liquid water will start to boil even at 300C.According to Bernoulli's theorem when the flow velocity increases, the pressure at that point drops. This increment in flow velocity may be due to reduction in cross-sectional area also. The reduction in pressure to the vapor pressure leads to boiling of the liquid and small vapor bubbles start to form. These vapor bubbles travel with the flowing liquid and collapse at the high-pressure zone resulting in damage to the metallic surface. This phenomenon is known as cavitation. Thus, in order to avoid cavitation, the pressure at any point in the flowing liquid should not drop to vapor pressureTo know more about standard light intensity visit : https://brainly.com/question/11864750
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19. Jorge was driving at 20m/s. He accelerated at a rate of 2m/s² for 10s. How far did he travel during this time?
Jorge was driving at 20m/s. He accelerated at a rate of 2m/s² for 10s.
So he travel ---m during this time.
Jorge was driving at 20m/s, so speed = 20 units
He accelerated at a rate of 2m/s² so acceleration = 2 units
Time taken by Jorge is 10 units.
We know by Newton's 2nd equation of motion that
S= ut + (1/2)*a*t*t
where S is distance, a is acceleration, u is initial velocity and t is time.
So S=?
Time t = 10
Acceleration a =2
Initial Velocity u = 20
Hence distance travelled by Jorge is S=300 m
Thus Jorge travelled 300m during this time at speed 20m/s accelerated at a rate of 2m/s² for 10s.
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the head of a nail is 0.39 cm0.39 cm in diameter. you hit it with a hammer with a force of 27 n.27 n. what is the pressure pheadphead on the head of the nail?
The pressure is 22.59 x 10⁵ Pa.
We need to know about pressure to solve this problem. Pressure is unit that describe how much force applied on a surface area. It can be determined as
P = F / A
where P is pressure, F is force and A is area.
From the question above, we know that
d = 0.39 cm = 0.0039 m
F = 27 N
Calculate the surface area of the nail
A = π . r²
A = π . (1/2 . d)²
A = π . (1/2 . 0.0039)²
A = 1.195 x 10¯⁵ m²
Determine the pressure
P = F / A
P = 27 / (1.195 x 10¯⁵ )
P = 22.59 x 10⁵ Pa
Hence, the pressure is 22.59 x 10⁵ Pa.
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An aquarium is 2 m long, 1 m wide, and 1 m deep is full of water weighing 9,800 n/m3.(a) find the work needed to pump half of the water out of the top of the aquarium
In an aquarium 2 m long, 1 m wide, and 1 m deep, the work needed to pump half of the water is 2452.5 J
CalculationWork done is defined as the integral of force multiplied with distance.
So, the formula goes as W=[tex]\int\limits^a_b {Fx} \, dx\\[/tex]
Force can be written in terms of density as
F = m * g = ρVg
v = 2x1x1 = 2[tex]m^{3}[/tex]
so, work done will be
W = [tex]\int\limits^{0.5}_0 2*1000*9.81* {x} \, dx[/tex]
= 19620[tex](\frac{x^2}{2} )\left \{ {{0.5} \atop {0}} \right.[/tex]
W = 19620 [tex]\frac{(0.5)^2}{2}[/tex]
W= 2452.5 J
Thus, the work that is needed to be done to pump half the water = 2452.5 J
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a solid sphere of radius 40.0 cm has a total positive charge of 31.9 µc uniformly distributed throughout its volume. calculate the magnitude of the electric field at the following distances.
The magnitudes of the electric field at the following distance 0cm,10cm,40cm,72cm are 0,5.2 x 105 N/C,2.1 x 106 N/C and 6.42 x 105 N/C.
What is an electric field?An electric field is a physical field that surrounds a charged particle and exerts a force on all other charged particles in the field to attract or repel each other. Electric fields are generated by electric charges and time-varying currents. Both electric and magnetic fields are manifestations of the electromagnetic field, one of nature's four fundamental interactions (also called forces). Electric fields are important in many areas of physics and are used in electrical engineering. For example, in atomic physics and chemistry, the electric field is the gravitational force that holds atomic nuclei and electrons together. It is also the force responsible for the chemical bonds between atoms that form molecules.
R = 40 cm = 0.4 m ; q = 31.9 \muC = 32 x 10-6 C ;
We need to find the expression for E field for given geometry.
from Gauss law,
(r). dA = Qin/ e0
E(r) \oint dA = Qin/ e0
E(r) . 4 pi r2 = Qin/ e0
E(r) = Qin/4 pi[tex]r^{2}[/tex]
For, Qin = Q (4 pi r3 / 4 pi R3) = Q (r/R)3 putting this in above equation
E(r) = Q r3/4 pir2
R3 = E(r) = Q r /4 piR3
E(r) = Q r /4 pi R3 (1)
For, Qin = Q
E(r) = Q/4 pi r2 (2)
(a) Since r = 0 is r < R
Using 1
E(r) = E(0) = 0
(b) r = 0.1 m
Again using 1
E(r) = Q r /4 piR3
E(0.1) = 9 x 109 x 37 x 10-6 x 0.1 / (0.4)3 = 5.2 x 105 N/C
Hence, E(0.1) = 5.2 x 105 N/C
(c) r = 0.4 m
We will use (2) here
E(r) = Q/4 pi r2
E(0.4) = 9 x 109 x 37 x 10-6 / (0.4)2 = 2.1 x 106 N/C
Hence, E(0.4) = 2.1 x 106 N/C
d)r =0.72 m
We will use (2) here
E(r) = Q/4 pi r2
E(0.72) = 9 x 109 x 37 x 10-6 / (0.72)2 = 6.42 x 105 N/C
Hence, E(0.4) = 6.42 x 105 N/C
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