A solid sphere of radius A has a uniform charge density per unit volume rho and a total charge Q. Express the result for E(r) for 0 ≤ r ≤ a in terms of Q and a instead of rho, and make a sketch of E(r) showing its behavior over both the ranges 0 ≤ r ≤ a and r ≥ a. (b) Place a particle with charge +q0 at a distance r1 > a from the center of the sphere. What is the work W1 done by the Coulomb force on the particle as the particle moves from r=r1 tor=[infinity]? (c)(Numeric)IfQ=1μC,q0 =10nC,a=0. 05m,andr1 =0. 2m,computeW1 basedon your result to part (b). [Ans. W1 = 4. 5 × 10−4 Joules. ] (d) Using the expression for change in potential energy ∆U = −W, and the convention that U(+[infinity]) = 0, obtain the expression U(r) for the potential energy of the charge q0 as a function of the distance r from the center of the sphere, for r ≥ a. (e) Recalling the definition of the electric potential V , write down the expression for V (r) due to the sphere for r ≥ a. (f) (Numeric). Using the same numerical values given in part (c), calculate the electric potential V (r = a) due to the sphere at the surface of the sphere. [Ans. V (r = a) = 1. 8×105 Volts. ] (g) Now, supposing the charge q0 starts from a position r2 < a, compute the work W2 done by the electric field inside the sphere in moving the charge q0 from r = r2 to the edge of the sphere at r = a. (h) (numeric) If r2 = 0. 03 m, compute W2 using the other numerical values from part (b). [Ans: W2 = 5. 8 × 10−4 Joules. ] (i) Again, using the expression for change in potential energy ∆U = −W , and the convention that U(+[infinity]) = 0, obtain the expression U(r) for the potential energy of the charge q0 as a function of the distance r from the center of the sphere, for r ≤ a. Write down the corresponding expression for V (r) in this same range. Is the electric potential higher inside the sphere than outside? (j) Using the numerical values we’ve been using, make computer generated plots of V (r) overtheranges0≤r≤aanda≤r≤5a. LookattheshapeofV(r)asr→0. Isit consistent with the electric field being zero at t
Answers
Given a solid sphere of radius A has a uniform charge density per unit volume ρ and a total charge Q, we need to find the electric field E(r) for 0 ≤ r ≤ a in terms of Q and a instead of ρ.
(b) Work done by the Coulomb force on the particle as the particle moves from r = r1 to r = infinity is W1.The charge q0 is positive, and therefore the direction of the force and displacement is radially outward from the center of the sphere. The work done by the Coulomb force on the particle as the particle moves from r = r1 to r = infinity is the same as the change in potential energy of the particle from r = r1 to r = infinity.
(c) For Q = 1μC, q0 = 10nC, a = 0.05m, and r1 = 0.2m, we can compute W1 based on the result from part (b) which is, W1 = 4.5 × 10−4 Joules.
(d) Let the charge q0 be at a distance r from the center of the sphere. Then, the potential energy of the charge q0 is given by U(r).∆U = −W, and the convention that U(+[infinity]) = 0Therefore, U(r) = −W, when q0 is at a distance r from the center of the sphere, U(+[infinity]) = 0.
(e) The electric potential V (r) due to the sphere for r ≥ a is given by, V (r) = U(r) / q0.
(f) Using the numerical values from part (c), we can compute the electric potential V (r = a) due to the sphere at the surface of the sphere which is, V (r = a) = 1.8×105 Volts.
(g) Let the charge q0 start from a position r2 < a. Then, the work done by the electric field inside the sphere in moving the charge q0 from r = r2 to the edge of the sphere at r = a is W2.
(h) For r2 = 0.03 m, we can compute W2 using the other numerical values from part (b) which is, W2 = 5.8 × 10−4 Joules.(i) The potential energy of the charge q0 as a function of the distance r from the center of the sphere, for r ≤ a is U(r).The corresponding expression for V (r) in this same range is given by, V (r) = U(r) / q0.Inside the sphere, the electric potential is higher than outside.
(j) A computer-generated plot of V (r) over the ranges 0 ≤ r ≤ a and a ≤ r ≤ 5a shows that the shape of V (r) as r → 0 is consistent with the electric field being zero at the center of the sphere.
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Related Questions
A poster is 0.95m high and 1.0m wide how many digits follow the decimal point when the perimeter of the poster is expressed with the correct number of significant figures
A) zero digits
B) one digit
C)two digits
D)three digits
Answers
Explanation:
It is given that,
Length of the poster, l = 0.95 m
Breadth of the poster, b = 1 m
The poster is in the shape of rectangle. For a rectangular shape, perimeter is equal to :
P = 2(l+b)
P=2(0.95+1)
P=3.9 m
(b) One digits, P = 4 m
(c) Two digits, P = 3.9 m
(d) Three digits, P = 3.90 m
A block weighing 100. newtons is positioned on an incline that makes an angle of 30.° with the horizontal. The magnitude of the friction force between the block and the incline is 10. newtons. A force of 120. newtons is applied by pulling on a rope that makes an angle of 30.° with the incline, as shown.
Draw a free-body diagram, and provide appropriate labels for each of the forces. (Optional)
Calculate the component of the block’s weight parallel to the incline.
Calculate the magnitude and direction of the component of the tension that is useful in moving the block up the incline.
Calculate the magnitude and direction of the block’s acceleration.
Answers
(a) The perpendicular component of the block's weight is 86.6 N.
(b) The parallel component of the block's weight is 50 N.
(c) The magnitude and direction of the tension needed to move the block is 103.9 N upwards.
(d) The magnitude and direction of the block's acceleration is 4.3 m/s² upwards.
What is the components of the block's weight?The perpendicular and parallel component of the blocks weight is calculated as follows;
The perpendicular component of the block's weight is calculated as follows;
W (n) = W cosθ
where;
W is the weight of the blockθ is the angle of inclination of the blockW (n) = 100 x cos(30)
W (n) = 86.6 N
The parallel component of the block's weight is calculated as follows;
W (p) = W sinθ
W (p) = 100 x sin (30)
W (p) = 50 N
The magnitude of the tension needed to move the block is calculated as follows;
T = F cosθ
where;
F is the applied forceθ is the angle of inclinationT = 120 x cos(30)
T = 103.9 N upwards
The acceleration of the block is calculated as follows;
T - Ff - W (p) = ma
where;
Ff is force of frictiona is accelerationm is the massm = W /g
m = 100 N / 9.8 m/s² = 10.2 kg
T - Ff - W (p) = ma
103.9 - 10 - 50 = 10.2a
43.9 = 10.2a
a = 43.9 / 10.2
a = 4.3 m/s² upwards
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An iron nail is more strongly attracted to the a) north pole of a magnet b) south pole of a magnet. c) north or south pole-no difference really
Answers
An iron nail is drawn to the magnet's north pole and adheres to it. The iron nail becomes a conduit for the magnetic field lines. As a result, the side that becomes attached to the North Pole serves as the South Pole.
Is an iron nail more drawn to a magnet's north or south pole?
A magnet's strength is greatest close to its poles. Therefore, the magnet's two poles will attract the greatest amount of nails.
An iron nail is more attracted to which pole of a magnet?
Iron nails are magnetically inducted to acquire the opposite polarity when they are brought close to one end of a magnet. Since opposing poles are drawn to one another,
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I need chapter one section three
Answers
If y = a + by + c(t)^2 where y = distance , t = time , find the dimension and unit of c.
Please help!!:)
Answers
\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)
\(\textsf{ \underline{\underline{Steps to solve the problem} }:}\)
In the given equation :
\( \qquad❖ \: \sf \:y = a + b + c( {t}^{2} )\)
If three physical quantities is to be added or subtracted, they must have same dimensions.
So, dimension of y = dimension of c(t²)
And we already know,
y = M⁰L¹T⁰ [ since it represents distance/length ]t = M⁰L⁰T¹ [ since it represents time ]t² = M⁰L⁰T²( by squaring )
Now, we need to calculate dimension and unit of c :
\( \qquad❖ \: \sf \:dim(y) = dim(c {t}^{2} )\)
\( \qquad❖ \: \sf \:M⁰L¹T⁰ = dim(c) \sdot M⁰L⁰T²\)
\( \qquad❖ \: \sf dim(c) = \frac{M⁰L¹T⁰}{ M⁰L⁰T²} \)
\( \qquad❖ \: \sf dim(c) = {M⁰L¹T {}^{ - 2} }\)
Now, we got the dimension of c as :
M⁰L¹T-²So, it's SI unit will be :
m/s²[ since SI unit of length/distance = m, and SI unit of Time = sec, hence SI unit of T² = s² ]
Question
If y = a + by + c(t)^2 where y = distance , t = time , find the dimension and unit of c.
\(\boxed{\green{c=M^0L^1T^{-2}}}\)
Solution Given:
We know that
Law of Homogeneity of Dimensions In any correct equation representing the relation between physical quantities, the dimensions of all the terms must be the same on both sides.
Dimension of Time is denoted by [T]
Dimension of distance is denoted by [L]
Dimension of mass is denoted by [M]
So,
Dimension of a, by, c(t)^2 should be equal to y.
y=[L] .......[1]
a=[L].......[2]
by=[L].......[3]
c(t)^2=[L].....[4]
Now
The dimension of c can be obtained as:
c(t)^2=[L]
c= \( \frac{[L]}{[T^2]}\)
\(\boxed{\green{c=M^0L^1T^{-2}}}\)
Sry for late!!
the electric field between the plates of an air capacitor of plate area 0.8 m^2 what is maxwell's displacement current
Answers
The electric field between the plates of an air capacitor of plate area 0.8 m^2 and the Maxwell's displacement current, we need additional information such as the distance between the plates and the voltage applied to the capacitor.
The electric field between the plates of a capacitor is given by the formula E = V/d, where V is the voltage applied to the capacitor and d is the distance between the plates. If we have the value of d and V, we can calculate the electric field.
Maxwell's displacement current, we need to know the rate of change of the electric field in the region between the plates of the capacitor. This can be difficult to determine without additional information about the circuit. However, we can say that the displacement current will be proportional to the rate of change of the electric field and the permittivity of free space. If we have the value of the electric field and the rate of change of the field, we can calculate the displacement current.
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Jibari walks 40. 0 meters east in 120. 0 seconds. He then walks 30. 0 meters west in 60. 0 seconds. What is his average velocity for the trip??
Answers
Answer:
0.389 meters per second
Explanation:
1. Get your knowns
a. 40 meters per 120 seconds
b. 30 meters per 60 seconds
2. Add
Total distance = 40 meters + 30 meters = 70 meters
Total time = 120 seconds + 60 seconds = 180 seconds
3. Divide
Average velocity = 70 meters / 180 seconds
= 7 meters / 18 seconds
= 0.388... meters per second
How far does a runner travel if they maintain a speed of 9.5 m/s for 140s?
Answers
Sub Science Project work
Represent an idea of to demonstrate your innovation on one of the following topic through practical.
Utilization of wastes
Model of plantation
Craft works for utilization and preservation Exploring energy sources.
Application based device
Answers
One innovative project idea related to the topic of exploring energy sources could be the development of a small-scale renewable energy system.
The project could involve designing and constructing a miniature model that demonstrates the utilization of renewable energy sources such as solar, wind, or hydroelectric power. The model could consist of solar panels to harness sunlight, a wind turbine to capture wind energy, or a small water turbine to generate electricity from flowing water. The energy generated by these sources could be stored in batteries or used directly to power various devices or components of the model.
The project could also incorporate an application-based device to monitor and control the energy system. This device could provide real-time data on energy production, consumption, and efficiency. It could also allow users to control the system remotely, adjust settings, and optimize energy usage.
By creating this practical demonstration, the project aims to raise awareness about the importance of renewable energy sources and promote sustainable energy practices. It provides an opportunity to showcase the potential of renewable energy and encourage further exploration and innovation in this field
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The data below were collected by scientists testing the force of gravity between two objects.
Distance Mass 1 Mass 2 Force
(kg) (kg)
(m)
(N)
0.10
100 150
0.00010
0.10
150
150
0.00015
0.10
100
300 0.00020
0.10
200
200
0.00027
0.10
200
300 0.00040
What do the data in the table support?
OA. The force of gravity between two objects is determined by the object with less mass.
OB. The force of gravity depends on the masses of the objects interacting.
OC.
The force of gravity between two objects is determined by the object with more mass.
D.
The force of gravity only depends on the distance between the objects interacting.
Answers
The data table supports that: Option B, "the force of gravity depends on the masses of the objects interacting." is the correct answer.
What is gravity?
Gravity, also sometimes called as gravitation, is the non-changing force of attraction that binds everything together in mechanics. Being the weakest known force in nature, it has little effect on determining the intrinsic properties of common objects.
In the given data table, the distance is same in all five cases, but we can see that the force of gravity is increasing with increase in mass of any one of the object or both of them. We can also understand it as the force of gravity is increasing with the increase in combined mass of both objects.
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ALGEBRA Find x and the measures of the unknown sides of each triangle.
12.
M
13.
R
17
Sx
6x - 5
2x + 7
2
N
O
5
3x - 4
3x + 10
+
Answers
9514 1404 393
Answer:
12. x = 11; sides are 29
13. x = 5; sides are 25
Explanation:
12. The marked sides are equal length, so ...
3x -4 = 2x +7
x = 11 . . . . . . . . add 4-2x
2x+7 = 2(11)+7 = 29 . . . side lengths
__
13. The marked sides are equal length, so ...
6x -5 = 5x
x = 5 . . . . . . . add 5-5x
5x = 5(5) = 25 . . . side lengths
Which soil conservation method involves planting different crops in a field
each year to restore nutrients.
Answers
Answer:
Crop rotation is the practice of growing a series of different types of crops in the same area across a sequence of growing seasons. It reduces reliance on one set of nutrients, pest and weed pressure, and the probability of developing resistant pest and weeds
what was his starting velocity???
Answers
Answer:
Vo = 18.3 [m/s]
Explanation:
To solve this problem we must use the following equation of kinematics.
\(v_{f} =v_{o} -a*t\)
Vf = final velocity = 0 (the bike stops)
Vo = initial velocity [m/s]
a = desacceleration = 6.42 [m/s²]
t = time = 2.85 [s]
Note: the negative sign in the above equation means that the motorcyclist decrease his velocity.
0 = Vo - (6.42*2.85)
Vo = 18.3 [m/s]
Please help
Will give the brainliest!
Answers
Answer:
both answer is option C
Explanation:
tag me brainliest
why is black the good absorber of radiation?
Answers
Answer:
=> Black colour do not reflect the wavelength of light and is a good emitter of heat . This, black is a good absorber of radiation.
Answer:
Black coloured objects absorb all the wavelengths of light and do not reflect any of them. Therefore, it looks black in colour and is considered to be a good absorber and a good emitter of heat. On the other hand, white coloured objects reflect all the light that falls into it and therefore they look white
PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP
I NEED TO GIVE THIS IN TODAY!!!
Answers
Answer:
a) greater
smaller
Explanation:
when light with a wavelength of 176 nm strikes the surface of tin metal, electrons are ejected with a maximum kinetic energy of j. what is the binding energy of these electrons to the metal?
Answers
The binding energy of electrons to the metal can be calculated using the equation:
Binding Energy = Planck's constant × speed of light / wavelength of light - Maximum kinetic energy of ejected electrons
First, convert the wavelength from nm to meters: 176 nm = 176 × 10^(-9) meters.
Next, use the equation E = hf to calculate the energy of one photon, where E is the energy, h is Planck's constant (6.626 × 10^(-34) J·s), and f is the frequency of light. Since frequency is the speed of light divided by wavelength, f = c / λ, where c is the speed of light (3.00 × 10^8 m/s) and λ is the wavelength of light.
Substitute the values into the equation and solve for energy.
Finally, subtract the maximum kinetic energy of the ejected electrons from the calculated energy to find the binding energy.
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2.) A rock is kicked off a 5m high cliff. The rock lands 7m from the base of the cliff. With what velocity was the rock initially kicked?
Answers
The velocity with which the rock initially kicked if the cliff is 5 m high and the rock lands 7m from the base of the cliff is 6.93 m / s
s = ut + 1 / 2 at²
s = Distance
u = Initial velocity
t = Time
a = Acceleration
In vertical motion,
s = 5 m
u = 0
a = 9.8 m / s²
5 = 0 + ( 1 / 2 * 9.8 * t² )
t² = 1.02
t = 1.01 s
In horizontal motion,
s = 7 m
a = 0 ( Since velocity is constant )
7 = 1.01 u + 0
u = 7 / 1.01
u = 6.93 m / s
Therefore, the velocity with which the rock initially kicked is 6.93 m / s
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what value offf freactance qx could be added to make the total load seen by the generator purely resistive
Answers
To make the total load seen by the generator purely resistive, the reactive component of the load must be canceled out. This can be achieved by adding a reactance with the opposite sign and equal magnitude to that of the reactive component of the load.
Let's assume that the load has a resistance R and a reactance X. The total impedance of the load is then given by Z = R + jX, where j is the imaginary unit.
To cancel out the reactive component of the load, we need to add a reactance -X in series with the load, which gives a total impedance of Z' = R + jX - jX = R. This means that the total load seen by the generator is purely resistive, with no reactive component.
Therefore, to find the value of reactance Qx that needs to be added, we just need to find the magnitude of the reactive component of the load, which is |X|. So, Qx = |X|.
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If you are lying down and stand up quickly, you can get dizzy or feel faint. This is because the blood vessels don't have time to expand to compensate for the blood pressure drop. If your brain is 0.4 m higher than your heart when you are standing, how much lower is your blood pressure at your brain than it is at your heart? The density of blood plasma is about 1025 kg/m3 and suppose your maximum (systolic) pressure of the blood at the heart is 116.4 mm of Hg (Note that 120 mm of Hg = 16 kP = 1.6 x 104 N/m2). Since most doctors still use mm of Hg, give your result in those units.
Answers
91.655 mm of Hg pressure is lower when our blood pressure at brain than it is at your heart.
pressure at brain= 121.8-30.135
pressure=91.655 mm Hg
Pressure is defined as force/area. To demonstrate the pressure from snow on a roof, divide the weight of the snow by the surface area of the roof. Gases are a typical pressure source in physics. A "vacuum" is used to describe the lack of pressure. Humans have long held the belief that vacuums are both improbably rare and unnatural since "nature abhors a vacuum." Actually, this is not the case.
The number of pressure units is ridiculous. It's common to use the torr or mmHg unit. This discussion is solely focused on the height of a mercury column. The atmosphere contains 760 torr, or mmHg. You could also look at mmH2O, which makes use of a comparable idea.
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water flows steadily along a uniform flow tube of cross section area 20cm². The total pressure is 3x104pa and static pressure is 2.5x104 pa. Calculate the velocity of the fluid.
please help me
Answers
steadily along a uniform flow tube of cross section area 20cm². The total pressure is 3x104pa and static pressure is 2.5x104 pa. Calculate the velocity of the fluid.
If the radius increased between the two objects what would happen to gravitational force between them?
Answers
Answer:
The Gravitational Force would decrease
Explanation:
The equation Gm1m2/r^2 is the equation for gravitational force. If you look, as we increase the radius, the overall value will decrease as we move further apart.
Which term best describes how the solar system formed?.
Answers
Answer:
Approximately 4.6 billion years ago, the solar system was a cloud of dust and gas known as a solar nebula.
Explanation:
The gravitational attraction between two objects is reduced most when –.
Answers
The gravitational attraction between two objects is reduced most when the distance between them is increased. According to Newton's law of universal gravitation, the force of gravity is inversely proportional to the square of the distance between two objects.
The formula for the gravitational force between two objects is F = G * (m1 * m2) / r², where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
As the distance (r) between the objects increases, the denominator (r²) in the formula becomes larger, resulting in a smaller force of gravity. This inverse square relationship means that even a small increase in distance can lead to a significant reduction in gravitational attraction.
For example, if the distance between two objects is doubled, the force of gravity becomes only one-fourth (1/2²) of its original strength. If the distance is tripled, the force becomes only one-ninth (1/3²), and so on.
This principle can be observed in various astronomical phenomena. For instance, the gravitational pull of the Sun on a planet decreases as the planet moves farther away in its orbit. Similarly, the Moon's gravitational pull on Earth is weaker than the Sun's because it is much closer to Earth.
In summary, the gravitational attraction between two objects is reduced most when the distance between them is increased. This inverse square relationship highlights the significance of distance in determining the strength of gravitational forces and has profound implications for understanding the dynamics of celestial bodies and other gravitational interactions.
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36) What is the formula for determining the amount of heat energy needed to change the temperature of an object
Answers
The formula for determining the amount of heat energy needed to change the temperature of an object is given by the equation Q = mcΔT, where Q represents the heat energy, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
The amount of heat energy needed to change the temperature of an object can be calculated using the formula Q = mcΔT. The variables in the equation have the following meanings: Q represents the heat energy, which is measured in joules (J); m is the mass of the object, typically measured in kilograms (kg); c is the specific heat capacity of the material, which is the amount of heat energy required to raise the temperature of one kilogram of the material by one degree Celsius (J/kg·°C); and ΔT is the change in temperature, measured in degrees Celsius (°C).
The formula states that the heat energy (Q) required is directly proportional to the mass of the object (m), the specific heat capacity (c) of the material, and the change in temperature (ΔT). By multiplying the mass, specific heat capacity, and temperature change, we can calculate the amount of heat energy needed to change the temperature of an object. This formula is applicable to various scenarios where heat transfer and temperature changes are involved, allowing for accurate calculations of heat energy requirements.
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I need to convert 234 terameters to nanometers using Dimensional Analysis. I know the answer is 2.34 x \(10^{23}\). How do I get there?
Answers
Explanation:
First, convert terameters to meters.
234 Tm × (10¹² m / Tm) = 234×10¹² m
Now convert meters to nanometers.
234×10¹² m × (10⁹ nm / m) = 234×10²¹ nm
In scientific notation, that's 2.34×10²³ nm.
help yall this is serious-
Answers
Answer:
convection: heat transfer by movement of currents inside a liquid, currents in the mantle, temp inside the house, red dye rises blue dye sinks,
radiation: heat from a bonfire, transfer of energy through space,
conduction: frying pan to cooking egg, candle heating up foil to chocolate chips
Explanation:
A condition that lifts a parcel of air to form cumulus clouds is
Answer
a. differential heating.
b. mountain barriers.
c. a cold front.
d. All of the above.
Answers
A condition that lifts a parcel of air to form cumulus clouds is differential heating.
Thus, Differential heating of the land and the water. Water changes temperature more slowly because it has a high specific heat, like the ocean. Land, particularly sandy beaches, has a low specific heat, therefore it warms up faster than water with the same amount of heat.
Our beach towels are blown away by this land-and-water combination, but it is also to blame for more extreme weather like monsoons and thunderstorms and heat.
The typical afternoon thunderstorm might be produced by sea breezes. For instance, the Florida peninsula is bordered by the ocean on both sides. Cool air from the Gulf of Mexico blows inland on the western side as a sea breeze. A sea wind from the Atlantic Ocean causes the same thing to occur on the eastern side and differential heating.
Thus, A condition that lifts a parcel of air to form cumulus clouds is differential heating.
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A football player pushes against another player trying to block him from moving any farther down the field. Which term best describes this example?
Negative work
Positive work
Negative force
Positive force
Answers
Answer:
NEGATIVE
Explanation:
Answer:
negative force
Explanation:
This is so because he needs more force inorder to block the other one.So he won't achieve any good force outcome
true or flase form is an element of design that describes volume and mass ; the three dimensional aspects of objects that take up space.
Answers
form is an element of design that describes volume and mass ; the three dimensional aspects of objects that take up space is True.
Form is an element of design that refers to the three-dimensional aspects of objects, including volume and mass. It describes the physical shape and structure of an object, emphasizing its spatial presence and how it occupies and interacts with space. Form plays a crucial role in creating visual interest, defining the character of objects, and shaping the overall composition in various design disciplines, such as architecture, industrial design, and sculpture.
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