Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering at a point P on its axis, at distance x away from the center of the ring. Now the charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius. How does the field Edisk produced by the disk at P compare to the field produced by the ring at the same point?Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering at a point P on its axis, at distance x away from the center of the ring. Now the charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius. How does the field Edisk produced by the disk at P compare to the field produced by the ring at the same point?

Answers

Answer 1

Answer:

* E_ring = [tex]k \ \frac{x}{(x^2+ y^2)^{3/2} } \ Q[/tex]

*E_ disk= 2kQ  [tex]\frac{1}{R^2} \ (1 - \frac{x}{(x^2+ R^2)^{1/2} } )[/tex]

Explanation:

Let's start by finding the electric field of the charged ring

in the attachment we can see a diagram of the system. Due to circular symmetry, the electric field perpendicular to the axis is canceled and only the electric field remains parallel to the axis.

            Eₓ = E cos θ          (1)

            E = k ∫  [tex]\frac{dq}{r^2}[/tex]

            cos θ = x / r

             

using the Pythagorean theorem

            r = [tex]\sqrt{x^2 + y^2}[/tex]

we substitute

            Eₓ = k ∫ [tex]\frac{dq}{x^2+y^2} \ \frac{x}{\sqrt{ x^2+y^2} }[/tex]

            Eₓ =  [tex]k \frac{x}{(c^2+y^2)^{3/2} }[/tex]   ∫ dq

             Eₓ = k \frac{x}{(c^2+y^2)^{3/2} }  Q

the ring's electric field

             E_ring = [tex]k \ \frac{x}{(x^2+ y^2)^{3/2} } \ Q[/tex]

Now let's find the electric field of the disk

The charge is distributed over the entire disk, so let's use the concept of charge density

              σ = [tex]\frac{dq}{dA}[/tex]

Let's approximate the disk as a group of rings, the width of each ring is dr, the area is

              dA = 2πr dr

               

we substitute

             σ = [tex]\frac{1}{2\pi r} \ \frac{dq}{dr}[/tex]

             dq = 2π σ r dr

we substitute in equation 1, where the electrioc field is of each ring

             Eₓ = [tex]k \int\limits^R_0 \ { \frac{x}{(x^2+r^2)^{3/2} } \ 2\pi \sigma \ r } \, dr[/tex]

             

if we use a change of variable

               dv = 2rdr

               v = r²

              Eₓ =  [tex]k x \pi \sigma \int\limits^a_b { \frac{1}{(x^2+v)^{3/2} } } \, dv[/tex]

we integrate

              Eₓ = k x π σ   [tex][ \frac{ (x^2 + r^2)^{-1/2} }{-1/2} ][/tex]

we value in the limits from r = 0 to r = R

              Eₓ = k π σ x  (-2) [ [tex]\frac{1}{ \sqrt{x^2+R^2} } - \frac{1}{x}[/tex]]

              Eₓ = 2π k  σ ([tex]1 - \frac{x}{(x^2 + R^2 ) ^{1/2} }[/tex]  )

 

             σ = Q/πR²

substitute

             Eₓ = 2 k Q/R² (1 - \frac{x}{(x^2 + R^2 ) ^{1/2} } )

             E_ disk= 2kQ  [tex]\frac{1}{R^2} \ (1 - \frac{x}{(x^2+ R^2)^{1/2} } )[/tex]

             

The two electric fields are

* E_ring = [tex]k \ \frac{x}{(x^2+ y^2)^{3/2} } \ Q[/tex]

*E_ disk= 2kQ  [tex]\frac{1}{R^2} \ (1 - \frac{x}{(x^2+ R^2)^{1/2} } )[/tex]

we can see that the functional relationship of the two fields is different


Related Questions

Why do we use copper wiring?

Answers

Explanation:

The lower the level of resistivity the more electrical conductivity a metal has. Copper has low resistivity, and therefore is an excellent conductor. Copper is also less oxidative than other metals

Define electromagnetism​

Answers

Answer:

the phenomenon of the interaction of electric currents or fields and magnetic fields.

is a branch of Physics, that deals with the electromagnetic force that occurs between electrically charged particles. The electromagnetic force is one of the four fundamental forces and exhibits electromagnetic fields such as magnetic fields, electric fields, and light.

ball A is dropped from a hot air balloon rising at a costant velocity of 14,7 m.s'1 at a height of 19,7 m above the ground.the ball took 1.5s to reach its maximum height and hits the ground after some time in air.ignore the effects of air resistanceUse the ground as zero reference.3.1.1calculate the maximum height reached by the ball above the ground​

Answers

Answer:

this slow site thinks the answer is a link

Explanation:

this was a week ago so i dont know if u still need help

10. A 50 kg bicyclist on a 10 kg bicycle speeds up from 5.0 m/s to 10 m/s.
(a) What was the total kinetic energy before accelerating? Full working out​

Answers

Answer:

T.K.E = 750 Joules.

Explanation:

Given the following data;

Initial velocity, u = 5m/s

Final velocity, v = 10m/s

Mass of bicyclist = 50kg

Mass of bicycle = 10kg

Total mass, Tm = 50 + 10 = 60kg

Kinetic energy can be defined as an energy possessed by an object or body due to its motion.

Mathematically, kinetic energy is given by the formula;

[tex] K.E = \frac{1}{2}mv^{2}[/tex]

Where;

K.E represents kinetic energy measured in Joules.

m represents mass measured in kilograms.

v represents velocity measured in metres per seconds square.

To find the total kinetic energy before accelerating simply means the kinetic energy due to the initial velocity and total mass;

[tex] T.K.E = \frac{1}{2}T_{m}U^{2}[/tex]

Substituting into the equation, we have;

[tex] T.K.E = \frac{1}{2}*60*5^{2}[/tex]

[tex] T.K.E = 30*25 [/tex]

T.K.E = 750 Joules.

10. John does 176 J of work lifting himself a distance of 0.40 m. How
much force must John apply to accomplish this?
O 440 m
O 440 J
O 440 N
O 70.4 J

Answers

The answer is 440N

Outline 3 disadvantages and advantage of water and alcohol as a template liquid​

Answers

Answer:

Advantages of mercury as a thermometric liquid.

-It is a good conductor of heat and therefore the whole liquid reaches the temperature of the surroundings quickly.

-It does not wet (cling to the sides of) the tube.

-It has a high boiling point

-It expands uniformly (linear expansion) and responds quickly to temperature changes, hence is sensitive.

-It has a visible meniscus.

Disadvantages

-Mercury is very poisonous.

-its expansively is fairly low

-it is expensive

-It has a high freezing point therefore it cannot be used in places where the temperature gets very low.

Alcohol has a thermometric fluid

-Alcohol expands uniformly.

-It has a low freezing point (-115 degreecentigrade) therefore it is very suitable for place where the temperature gets very low.

-It has a large expansively

-It is an easily available cheap liquid, which is safe to use

Disadvantages of alcohol

-it wets the tube

-it has a low boiling point (cannot be used in places with high temperatures)

-it does not react quickly to changes in temperature

-It needs to be dyed, since it's colourless.

Disadvantages of water

-Water has high specific heat capacity. So it cannot be used for measuring small temperature differences.

- Water will wet the surface of the glass tube. It is a sticky substance.

- Water is transparent

Explanation:

The bus lay 40 km at a speed of 72 km / h, and then another 60 km at a speed of 30 m / s. Determine the average speed of the bus along the way.

Answers

Answer:

25 m/s

Explanation:

From the question,

Average speed = Total distance /total time.

S' = D/T........................... Equation 1

D = 40+60 = 100 Km = 100000 m.

T = t₁+t₂

t₁ = (40×3600/72) s = 2000 s

t₂ = 60000/30 = 2000 s

T = 2000+2000 = 4000 s.

SUbstitute the values of T and D into equation 1

S' = 100000/4000

S' = 25 m/s

Explain why the sound waves always reach the observer after the light waves

Answers

Answer:

I think it's because the light waves travel faster than the sound waves.

The speed of light is far greater than the speed of sound hence, sound waves always reach the observer after the light waves.

What is the speed of light?

Light occurs in the electromagnetic spectrum. Recall that light can be transmitted through vaccuum unlike sound.

The speed of light is far greater than the speed of sound hence, sound waves always reach the observer after the light waves.

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3. A backpack weighs 8.2 N and has a mass of 5 kg on the moon. What is t
strength of gravity on the moon?
8.2 N

Answers

Weight is equivalent to the product of the mass of an object and the strength of the gravitational field.

Using:
F = ma

a = 8.2 / 5
a = 1.64 N/kg

The gravitational field strength is equivalent to 1.64 N/kg.


C
D
7
The sun is the original source of
energy for many of our energy
resources
Which energy resource does not
originate from the sun? *
(1 Point)
.
A. Geothermal
B. Hydroelectric
C. Waves
D. Win

Answers

Answer:

geothermal

Explanation:

geothermal energy is the heat energy obtained from within the Earth. Hence not derived from Sun's energy.

A 1.6 kg ball is attached to the end of a 0.40 m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point of its swing, when it is moving horizontally, the ball collides with a 0.80 kg block that is at rest on a horizontal frictionless surface. The speed of the block just after the collision is 3 m/s. What is the speed of the ball just after the collision

Answers

Answer:

the speed of the ball just after the collision is 1.5 m/s.

Explanation:

Given;

mass of the ball, m₁ = 1.6 kg

initial velocity of the ball, u₁ = 0

mass of the block, m₂ = 0.8 kg

initial velocity of the block, u₂ = 0

final velocity of the block, v₂ = 3 m/s

let the final velocity of the ball after collision = v₁

Apply the principle of conservation of linear momentum for elastic collision;

m₁u₁ + m₂u₂ = m₁v₁  +  m₂v₂

1.6 x 0   +    0.8 x 0       =   1.6 x v₁     +  0.8 x 3

0 = 1.6v₁  + 2.4

-1.6v₁ = 2.4

v₁  = -2.4 / 1.6

v₁ = - 1.5 m/s

v₁ = 1.5 m/s (in opposite direction of the block)

Therefore, the speed of the ball just after the collision is 1.5 m/s.

Which water on earth is the largest,second to the largest,3rd to the largest,fourth to the largest and 5th to the largest?​

Answers

Answer:

Explanation:

There are a total of 5 differen classification for the types of bodies of water that exist on Earth. These 5 would be the following: Oceans, seas, lakes, rivers, and canals. Oceans are the biggest bodies of water on Earth. If we ranked them by their size the ranking would be the following...

Pacific Ocean - being 155,556,651 sq km. in size

Atlantic Ocean - being 76,761,938 sq km. in size

Indian Ocean - being 68,555,923 sq km. in size

Antarctic / Southern Ocean - being 20,327,001 sq km. in size

Arctic Ocean - being 14,055,930 sq km. in size

PLEASE HELP ME WITH THIS ONE QUESTION
How many joules are needed to vaporize 125 g of liquid water at 100°C? The latent heat of vaporization is 2258 J/g.

Answers

Answer:

Q = 282,000 J

Explanation:

Given that,

The mass of liquid water, m = 125 g

Temperature, T = 100°C

The latent heat of vaporization, Hv = 2258 J/g.

We need to find the amount of heat needed to vaporize 125 g of liquid water. We can find it as follows :

[tex]Q=mH_v\\\\Q=125\ g\times 2285\ J/g\\\\Q=282250\ J[/tex]

or

Q = 282,000 J

So, the required heat is 282,000 J .

In fatal crashes, more than __________% of passenger car occupants who were totally ejected from the vehicle were killed.

Answers

Answer:

it would be 83% in a fatal crash.

Why do scientists perform multiple trials of the same experiment?

Answers

Answer:

it's a good idea to do multiple trials, that is, do the same experiment lots of times. When we do multiple trials of the same experiment, we can make sure that our results are consistent and not altered by random events. Multiple trials can be done at one time.

Explanation:

the last one which is to increase the likelihood of accurate experiment results

Explanation:

Match the following items.
1. Extremely small building blocks of matter.
2. Forming new matter from old matter.
3. Small bits of matter.

atom
molecule
chemical change

Answers

1. atom
2. chemical change
3. molecule
hope this helps please mark branliest tyyyy!! <3

A marching band consists of rows of musicians walking in straight, even lines. When a marching band performs in an event, such as a parade, and must round a curve in the road, the musician on the outside of the curve must walk around the curve in the same amount of time as the musician on the inside of the curve. This motion can be approximated by a disk rotating at a constant rate about an axis perpendicular to its plane. In this case, the axis of rotation is at the inside of the curve. Consider two musicians, Alf and Beth. Beth is four times the distance from the inside of the curve as Alf. Knowing that If Beth travels a distance s during time Δt, how far does Alf travel during the same amount of time= (1/4)s

If Alf moves with speed v, what is Beth's speed?

a. 4v
b. v
c. v/4

Answers

Answer:

A) Total distance Alf travel during the same amount of time = [tex]\frac{1}{4}s[/tex]

B) Speed of Beth = 4v

Explanation:

Given - Consider two musicians, Alf and Beth. Beth is four times the

            distance from the inside of the curve as Alf.

To find - A) Knowing that If Beth travels a distance s during time Δt, how

                   far does Alf travel during the same amount of time.

              B) If Alf moves with speed v, what is Beth's speed?

Proof -

A)

As we know that

Speed = Distance / Time

⇒Distance = Speed ×Time

Now,

Given Speed of Alf = v

⇒Distance of Alf = vt

Also,

Distance of Beth = Speed of beth×time

Given that

Beth is four times the distance from the inside of the curve as Alf. Knowing that If Beth travels a distance s during time Δt, how far does Alf travel during the same amount of time=

⇒Distance of Alf = Speed of Alf×time

                           =  [tex]\frac{1}{4}[/tex] Distance of Beth

⇒Distance of Alf = [tex]\frac{1}{4}s[/tex]

∴ we get

Total distance Alf travel during the same amount of time = [tex]\frac{1}{4}s[/tex]

B)

We know the conversion of angular velocity

ω(Alf) = ω(Beth)

⇒V(Alf)/ r = V(Beth)/4r

⇒V(Alf) = V(Beth) / 4

⇒V(Beth) = 4 V(Alf)

As given, Alf moves with speed v

⇒V(Beth) = 4v

So, the correct option is - a.4v

Can you help me please here is the picture DUE NOW PLEASE.

Answers

they are formed when hot

it's dependent on the rate of cooling of the melt, slow cooling allows large crystals to form, fast cooling yields small crystals. They cool too quickly to form crystals.

Hope this helps! <3 :3

Young's double slit experiment is one of the quintessential experiments in physics. The availability of low cost lasers in recent years allows us to perform the double slit experiment rather easily in class. Your professor shines a green laser (560 nm) on a double slit with a separation of 0.108 mm. The diffraction pattern shines on the classroom wall 3.0 m away. Calculate the fringe separation between the third order and central fringe.

Answers

Answer:

 y = 4.666 10⁻² m

Explanation:

The constructive interference experiment for the double slit

         d sin sin θ = m λ

Let's use trigonometry to find a sine relationship.

         Tan θ = y / L

          tan θ = sin θ/ cos θ

in these experiments the angles are very small

           tan θ = sin θ

           sin θ = y / L

            [tex]d \frac{y}{L}[/tex] = m λ

              y = [tex]\frac{ m \lambda \ L}{d}[/tex]

we replace the values

              y = 3  560 10⁻⁹ 3.0 / 0.108 10⁻³

              y = 4.666 10⁻² m

A 65 kg cart travels at a constant speed of 4.6 m/s. What is its kinetic energy?

Answers

Answer:

Explanation:

mass (m) = 65 kg

velocity (v) = 4.6 m/s

Kinetic energy (KE)

= 1/2 * m * v²

= 1/2 * 65 * 4.6²

=  687.7 J

hope it helps :)

Which of the following is an example of the transformation of gravitational potential energy into motion energy (kinetic energy)?

Answers

Answer:

c

Explanation:

because a drop of water is falling and that is gravitational potential energy into motion energy

4. If the cooling of magma takes place slowly beneath Earth's surface, the rock is that is formed
is called
a. extrusive igneous rock
b. intrusive igneous rock
c. sedimentary rock
d. metamorphic rock

Answers

I agree with the answer above listen to them :)

Which is a primary energy source used by power plants to generate electricity?
coal
O wood
o gasoline
batteries

Answers

Answer:

Your answer is wood that is what they used

The primary energy source used by power plants to generate electricity is coal.

What are power plants?

Power plants are plants which use fuels to generate electricity for use by homes and industries.

Power plants have different energy sources for their fuel.

The primary energy source used by power plants to generate electricity is coal.

Therefore, coal is a primary source of fuel for power plants.

Learn more about power plants at: https://brainly.com/question/16064039

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5j-Tj=6j+3 Tj
Determine the value of T from the given vector

Answers

-1/4

Solve for j and Tj than you have
-j=4Tj
4T=-j/j
4T=-1
T=-1/4

What color is a carrot?

Answers

Answer:

reddish-orrange

Explanation:

please mark me as brainliest

A baseball is traveling (+30m/s) and is hit by a bat. It leaves the bat traveling (−40m/s). What is the change in its velocity?
Unlike some others, this is any choice, so not just 4 choices!

Answers

Answer:

Explanation:

The change must be 30 - - 40 which means it came in a 30 meters / second and went out in the opposite direction at 40 meters / second

The change is 70 m/sec.

You could show it to be - 70 meters per second as well. That's done by making the outgoing direction minus.

Delta v = vf - vi.

Now it depends on which way you define vf and vi.

. Four railroad cars, each of mass 2.50 104 kg, are coupled together and coasting along horizontal tracks at a speed of vi toward the south. A very strong but foolish movie actor, riding on the second car, uncouples the front car and gives it a big push, increasing its speed to 4.00 m/s southward. The remaining three cars continue moving toward the south, now at 2.00 m/s. (a) Find the initial speed of the cars. (b) How much work did the actor do

Answers

Answer:

a)     v₀ = 2.5 m / s,   heading south.

b)  W = 1,219 10⁵ J

Explanation:

a) For this exercise we can use the conservation of the moment, we create a system formed by all the 4 cars, in this case when the last one separates the forces are intense and the moment is conserved

initial instant. Before separation

        p₀ = M v₀

final instant. When uncoupling the last car

        p_f = 3m v₁ + m v₂

where they indicate that the speed of the wagons is v₁ = 2.00 m / s and the speed of the last wagon is v₂ = 4.00 m / s

the total mass is M = 4m

how the moment is preserved

           p₀ = p_f

         4m v₀ = 3m v₁ + mv₂

         v₀ = ¾ v₁ + v₂ / 4

let's calculate

           v₀ = ¾ 2 + ¼ 4

           v₀ = 2.5 m / s

heading south.

b) work is equal to the change in kinetic energy

              W = ΔK = K_f -K_o

              W = ½ m v_f² - ½ m v₀²

               W = ½ m (v_f² -v₀²)

               W = ½ 2.50 10⁴ (4² - 2.5²2)

               W = 1,219 10⁵ J

Need a little help here, ASAP please. The subject is simple science, not physics.

Answers

Shape, because a liquid can have mass, volume, and color, but it cannot have a definitive shape

True or false—If a rock is thrown into the air, the increase in the height would increase the rock’s kinetic energy, and then the increase in the velocity as it falls to the ground would increase its potential energy.

Answers

I think that this is false but I am not sure

If a rock is thrown into the air, the increase in the height would increase the rock’s kinetic energy, and then the increase in the velocity as it falls to the ground would increase its potential energy. _ This is false statement.

What is projectile motion?

When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's center (we assume the particle stays close to the surface of the globe). Such a particle's motion is known as projectile motion, and its route is referred to as a projectile.

In projectile motion total energy is conserved. Hence, when a rock is thrown into the air, the increase in the height would increase the rock’s potential energy, and then the increase in the velocity as it falls to the ground would increase its kinetic energy.

Learn more about projectile motion here:

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NEED HELP What color is the container for R-134a refrigerant? A. Light blue B. Yellow C. Dark green D.White and yellow​

Answers

Answer:

It is A. Light blue

_____________

Hope this helps!

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