A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume r. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density r. (b) What is the electric field at a point outside the volume in terms of the charge per unit length l in the cylinder

Answers

Answer 1

Answer:

Explanation:

From the given information.

The charge density of the cylinder can be computed as:

[tex]\rho = \dfrac{Q_t}{V_t}[/tex]

where:

[tex]Q_t[/tex] = total charge on cylinder

[tex]\rho[/tex] = density of the cylinder

[tex]V_t =[/tex] net volume on cylinder

Considering the charge enclosed by the Gaussian surface; we have:

Q = ρV

Now, determining the volume of the cylinder at a distance r from the axis of the cylinder as follows:

[tex]\int Edsn = \dfrac{q}{\varepsilon_o}[/tex]

Here;

[tex]\hat E \ \ and \ \ \hat n[/tex] are in the same direction;

If we replace [tex]\int Edsn[/tex] with [tex]E ( 2 \pi rl)[/tex] and q with [tex]\rho \pi r^2 l[/tex]; Then:

[tex]E ( 2 \pi rl ) = \dfrac{\rho \pi r^2 l}{\varepsilon _o}[/tex]

By rearrangement;

[tex]E = \dfrac{\rho \pi r^2 l}{ ( 2 \pi rl ) \varepsilon _o}[/tex]

[tex]\mathbf{E = \dfrac{\rho r}{ 2 \varepsilon _o}}[/tex]

(b)

Using the same formula:

[tex]\int Edsn = \dfrac{q}{\varepsilon_o}[/tex]

where;

[tex]\hat E \ \ and \ \ \hat n[/tex] are in the same direction;

If we replace [tex]\int Edsn[/tex] with [tex]E ( 2 \pi rl)[/tex] and [tex]Q_t[/tex] with q;

Then:

[tex]E ( 2 \pi rl ) = \dfrac{Q_t}{\varepsilon _o}[/tex]

[tex]E = \dfrac{Q_t}{( 2 \pi R l ) \varepsilon _o}[/tex]

Replacing [tex]\lambda[/tex] for [tex]\dfrac{Q_t}{l}[/tex].

From above [tex]\lambda[/tex] = the charge per unit length

[tex]\mathbf{E = \dfrac{\lambda}{ 2 \pi R \varepsilon _o}}[/tex]


Related Questions

Which have the same velocity?

A. A boy walking east at 2 km/h and a man walking east at 4 km/h
B. A car standing still and a truck driving in a circle at 4 km/h
C. A dog walking west at 3 km/h and a cat walking west at 3 km/h
D. A girl walking west at 3 km/h and a boy walking south at 3 km/h

Answers

Answer:

answer is b

Explanation:

Which equation will tell you the acceleration of the object?

Answers

Answer:

In summation, acceleration can be defined as the rate of change of velocity with respect to time and the formula expressing the average velocity of an object can be written as: a =Δ v/ Δt The other 4 equations: d = vit+ (1/2) at2

Explanation:

A toaster has a resistance of 30 ohms. It draws 2A of current from the outlet. What is the potential difference ?
A. 60v
B. 2v
C. 15v
D.30v

Answers

Answer:

60V

Explanation: . V = IR = 1

30*2=60

A car company is doing crash tests and has installed forcesensors in the chairs and seatbelts to measure the forces thatare exerted on crash test dummies during a crash. In oneparticular test the sensors measure a horizontal net force onthe dummy of 39,400 N when the car comes to a complete stopfrom an initial speed of 35 m/s in 1.4 m. Treating the dummyas a point particle and assuming it comes to rest in the samedistance, what is the mass of the test dummy used during thistest

Answers

Answer:

[tex]m=90.1kg[/tex]

Explanation:

From the question we are told that

Force F=39400

Initial speed [tex]V_1=35m/s[/tex]

Distance[tex]d=1.4m[/tex]

Generally the equation for acceleration is mathematically given by

[tex]a=\frac{V^2-U^2}{2d}[/tex]

[tex]a=\frac{0^2-35^2}{21.4}[/tex]

[tex]a=\frac{0^2-35^2}{21.4}[/tex]

[tex]a=-437.5m/sec^2[/tex]

Generally the equation for mass is mathematically given by

[tex]F=ma\\m=F/a[/tex]

[tex]m=\frac{-39400}{-437.5}[/tex]

[tex]m=90.1kg[/tex]

Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.

Answers

This question is incomplete, the complete question is;

A positive charge of magnitude Q1 = 6.5 nC is located at the origin.

A negative charge Q2 = -3.5 nC is located on the positive x-axis at x = 16.5 cm from the origin. The point P is located y = 10.5 cm above charge Q2.

Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.

Answer:

the x-component of the electric field at point P due to charge Q1 is 1291.33 N/C    

Explanation:

Given the data in the question;

Q1 = 6.5 nC, Q2 = -3.5 nC

from the image below, to get our angle ∅

tan∅ = opp/adj

tan∅ = 10.5 / 16.5

tan∅ = 0.636363

∅ = tan⁻¹( 0.636363 )

∅ = 32.47°

also, r1 = √( 16.5² + 10.5²)

r1 = √( 272.25 + 110.25 )

r1 = √382.5

r1 = 19.55 cm = 0.1955 m

Now, the x-component of the electric field at point P due to charge Q1 will be;

Ex = E2cos32.47°

= (kQ1/r1²)cos32.47°

we know that;  k is Coulomb's law constant ( 9 × 10⁹ N.m²/ C²

Q1 = 6.5 nC = 6.5 × 10⁻⁹ C

so we substitute

= ((9 × 10⁹ × 6.5 × 10⁻⁹) / (0.1955)²) cos32.47°

= (58.5 / 0.03822025) × 0.843672

= 1291.33 N/C

Therefore, the x-component of the electric field at point P due to charge Q1 is 1291.33 N/C

Consider a 2 m wide and 5 m long slab resting on flat, fixed, earthen bed. The slab is 20 cm thick with uniform properties. You may assume the slab is much longer and wider than it is thick. Write the reduced form of the governing equation for the slab. Clearly identify your coordinate system on a sketch and state your assumptions identifying which terms you are eliminating and why.

Answers

Answer:

Explanation:

The coordinate sketch for the system is shown in the attached file below. Also, in the cartesian coordinate system, since the height is less than the length and width, we did neglect the height. Thus, we eliminate the height and converted it to a two-dimension.

during what part of their drive are the not moving?

Answers

C answer is c math ez
The correct answer is c

Please answer this question correctly

Answers

20 push ups

hope thats correct^^

What is the kinetic energy of a 30 kg dog that is running at a speed of 8.6 m/s (about 19 mi/h)?

Answers

Answer:

Uhm thags hsed

Explanation:

Dkrr

how does different color show exist

Answers

Answer:Light is made up of wavelengths of light, and each wavelength is a particular colour. The colour we see is a result of which wavelengths are reflected back to our eyes. The visible spectrum showing the wavelengths of each of the component colours. The spectrum ranges from dark red at 700 nm to violet at 400 nm.  

Explanation:

hope it helps

Answer:When light hits an object, the object reflects some of that light and absorbs the rest of it. Some objects reflect more of a certain wavelength of light than others. That's why you see a certain colour. For example, a lemon reflects mainly yellow light.

Explanation:

A 30kg uniform solid cylinder has a radius of 0.18m. if the cylinder accelerates at 0.023 rad/s^2 as it rotates about an axis through its center, how large is the torque acting on the cylinder? With work please

Answers

Answer:

0.011 N-m

Explanation:

Given that

The mass of a solid cylinder, m = 30 kg

The radius of the cylinder, r = 0.18 m

The acceleration of the cylinder, [tex]\alpha =0.023\ rad/s^2[/tex]

It rotates about an axis through its center. We need to find the torque acting on the cylinder. The formula for the torque is given by :

[tex]\tau=I\alpha[/tex]

Where

I is the moment of inertia of the cylinder,

For cylinder,

[tex]I=\dfrac{mr^2}{2}[/tex]

So,

[tex]\tau=\dfrac{mr^2\alpha }{2}\\\\\tau=\dfrac{30\times (0.18)^2\times 0.023 }{2}\\\\\tau=0.011\ N-m[/tex]

So, the required torque on the cylinder is 0.011 N-m.

Why won’t anyone help me please anybody help me I really need help .

Answers

Answer:

1➡️ this is the method of decomposition

2➡️ H2 and O2

3➡️ b

sorry if I am wrong

A man standing on the Earth can exert the same force with his legs as when he is standing on the moon. We know that the mass of the man is the same on the Earth and the moon. We also know that F=ma is true on both the Earth and the moon. Will the man be able to jump higher on the moon than the Earth? Why or why not?
PLEASE HELPPPP

Answers

Answer:

yes

Explanation:

earth has gravity force that is high than the moon gravity force which is 1/6 of earth gravity

Earth has gravity force that is high than the moon gravity force which is 1/6 of earth gravity.

What is force?

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

The force on the moon is less than earth as gravity is 1/6 on the moon

When man jump than he will jump high on the moon than the earth.

Earth has gravity force that is high than the moon gravity force which is 1/6 of earth gravity.

To learn more about force refer to the link:

brainly.com/question/13191643

#SPJ2

The floor on a dance hall can take a pressure of 3.5MPa before getting damaged. A lady of mass 60kg wears high heeled shoes. What is the smallest area of the sole of a heel she could wear such that it won't permanently damage the floor

Answers

Answer:

smallest area of the heel is 0.000168  m^2

Explanation:

Recall that pressure is defined as: Force / area. Therefore to reach a pressure of 3,500,000 Pa using a force: m * g = 60 kg * 9,8 m/s^2 = 588 N, one needs:

Area = 588 / 3500000 m^2 = 0.000168  m^2

1. Two boxes stacked on top of one another weigh 100 kg total. They apply
a friction force of 250N. You apply a force of 300N in the right direction.
What is the total net force and direction of the box?

Answers

Answer:

150

Explanation:

Someone please please please help me with this. I’ll give u whatever rating u want

Answers

The vertical forces add up to zero.

The net force on the object is 60N to the right.

F = m • a

60N right = (10kg) • (a)

a = (60N right) / (10kg)

a = 6 m/s^2 to the right

Multi-engine Commercial would be nice.

Galileo is considered the father of modern science. Do you agree with this description? Give reasons for your answer.

Answers

Answer:

Galileo Galilei pioneered the experimental scientific method and was the first to use a refracting telescope to make important astronomical discoveries

Explanation:

Yes I agree with this. He made significant scientific discoveries that changed the way of life.

inertia is a measure of
a) a push or pull on an object
b) the difficulty of changing an object's motion
c) a velocity of an object
d) none of the above

Answers

Answer:

b.. a difficulty of changing an object's motion, that's my ✨ g u e s s ✨

Orchestra instruments are commonly tuned to match an A-note played by the principal oboe. The Baltimore Symphony Orchestra tunes to an A-note at 440 Hz while the Boston Symphony Orchestra tunes to 442 Hz. If the speed of sound is constant at 343 m/s, find the magnitude of difference between the wavelengths of these two different A-notes. (Enter your answer in m.)

Answers

Answer:

Δλ = 3*10⁻³ m.

Explanation:

At any wave, there exists a fixed relationship between the speed of  the wave, the wavelength, and the frequency, as follows:

       [tex]v = \lambda* f (1)[/tex]

       where v is the speed, λ is the wavelength and f is the frequency.

Rearranging terms, we can get λ from the other two parameters, as follows:

       [tex]\lambda = \frac{v}{f} (2)[/tex]

Since v is constant for sound at 343 m/s, we can find the different wavelengths at different frequencies, as follows:

        [tex]\lambda_{1} =\frac{v}{f_{1}} = \frac{343m/s}{440(1/s)} = 0.779 m (3)[/tex]

        [tex]\lambda_{2} =\frac{v}{f_{2}} = \frac{343m/s}{442(1/s)} = 0.776 m (4)[/tex]

The difference between both wavelengths, is just the difference between (3) and (4):

       [tex]\Delta \lambda = \lambda_{1} - \lambda_{2} = 0.779 m - 0.776m = 3e-3 m (5)[/tex]

       ⇒ Δλ = 3*10⁻³ m.

1) The cause of magnetism is
A. atoms forming “domains” that are arranged randomly
B. atoms forming "domains” that are arranged uniformly
C. atoms forming "dolomites” that are arranged randomly
D. atoms forming “dolomites” that are arranged uniformly

Answers

Answer:

I think it's A, I'm not sure though

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