A planar insulating sheet with an infinitesimal thickness has charge per unit area σ and is parallel to the x−z plane, as shown. (The arrows indicate that the object extends for a long distance in the horizontal plane.) By the symmetry of the problem, the electric field may be expressed as E⃗ =Ej^. This problem relates the change in the electric field from the lower side to the upper side of the insulating sheet to the surface charge density.

a) Enter a vector expression, in Cartesian unit-vector notation, for the electric field at points just above the planar insulating sheet.
b)Enter a vector expression, in Cartesian unit-vector notation, for the electric field at points just below the planar insulating sheet.

Answers

Answer 1

a. The electric field above the planar insulating sheet is Ej = (σ/ε₀)j

b. The electric field below the planar insulating sheet is -Ej = -(σ/ε₀)j

a. Electric field above planar insulating sheet

The electric field above the planar insulating sheet is Ej = (σ/ε₀)j

Gauss's law

Using Gauss' law ε₀∫E.dA = q where

ε₀ = permittivity of free space, E = electric field vector normal to the surface above the planar insulating sheet = Ej, dA = normal vector to surface above the planar insulating sheet = dAj, q = charge enclosed by Gaussian surface on planar insulating sheet = σA where σ = surface charge density and A = area of surface

Now, ε₀∫E.dA = q

ε₀∫Ej.dAj = σA

ε₀∫EdA = σA

ε₀E∫dA = σA

ε₀EA = σA

ε₀E = σ

E = σ/ε₀

So, the electric field above the planar insulating sheet is Ej = (σ/ε₀)j

b. Electric field above below insulating sheet

The electric field below the planar insulating sheet is -Ej = -(σ/ε₀)j

Gauss's law

Using Gauss' law ε₀∫E.dA = q where

ε₀ = permittivity of free space, E = electric field vector normal to the surface below the planar insulating sheet = -Ej, dA = normal vector to surface below the planar insulating sheet = -dAj, q = charge enclosed by Gaussian surface on planar insulating sheet = σA where σ = surface charge density and A = area of surface

Now, ε₀∫E.dA = q

ε₀∫-Ej.-dAj = σA

ε₀∫EdA = σA

ε₀E∫dA = σA

ε₀EA = σA

ε₀E = σ

E = σ/ε₀

So, the electric field below the planar insulating sheet is -Ej = -(σ/ε₀)j

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Related Questions

A skydiver has a mass of 80 kg. When she is at a height of 900 m, her GPE is
705,600 J. She is falling at a velocity of 32 m/s downward. What is her ME at this
point?

Answers

Answer:

11.25 J

Explanation:

GPE=wxh=80kg over 900m=11.25 J

Which of the following statements about charging objects is FALSE. Select one: If an object gains electrons it becomes positively charged. If an object gains electrons it becomes negatively charged. Charges cannot travel in an insulator. Charges can travel in a conductor.

Answers

Answer:

If an object gains electrons it becomes positively charged.

Explanation:

Electrons negatively charge.

a girl on a bridge throws a rock straight down at -12.5 m/s. it hits the ground 38.4 m below. How much time did it take?

Answers

Initial velocity=u=12.5m/sDistance=s=38.4mTime be t

[tex]\\ \rm\rightarrowtail s=ut+\dfrac{1}{2}gt^2[/tex]

[tex]\\ \rm\rightarrowtail 38.4=12.5t+4.9t^2[/tex]

On solving further we get

t=1.8s

A girl on a bridge throws a rock straight down at -12.5 m/s.the time required to hit the ground 38.4 m below is 4.35 s.

Given:

Speed, u = -12.5 m/s

Distance, d = 38.4 m/s

There are three equations of motion present. For the given question, we will use the second equation of motion.

The second equation of motion helps in the determination of velocity, time, and distance. For the given question, we have initial velocity, and distance, to find time we can use the second equation of motion.

From the second equation of motion:
[tex]s = ut + 1/2 at^2\\38.4 = -12.5t - 9.8/2* t^2\\\4.9t^2 - 12.5 t -38.4 = 0[/tex]

Solving the equation, the required time is:
[tex]t = 4.35 s[/tex]

Hence, the time required to hit the ground 38.4 m below is 4.35 s.

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what is true about a horizontally launched projectile?

Answers

Answer:

it has lateral momentum

Explanation:

it explains itself

differentiate kinetic energy from potential energy

Answers

The main difference between potential and kinetic energy is that one is the energy of what can be and one is the energy of what is. In other words, potential energy is stationary, with stored energy to be released; kinetic energy is energy in motion, actively using energy for movement.

Hope it helps you! :)

Answer:

Potential energy is the energy that happens before kinetic energy, it might be slow and preparing for the kinetic energy act. Kinetic energy is the outcome of the potential energy. You can say a man climbing a hill with his bike is potential energy, and when he rides his bike down is kinetic energy

Solar energy can be directly converted to elec-trical energy by which of the following de-vices?​

Answers

Answer: (c) solar cell

Explanation:

Answer:
A solar cell takes solar energy directly from the sunlight and converts it into electrical energy

29N, 60° +59N, 125° + 72N, 261°
Vectors

Answers

389wujh

which means it 240C

1. You set the thermostat in your house to 70 degrees so that when it goes above that temperature the air conditioner will turn on. What is the feedback of this system? 2. You set the thermostat in your house to 70 degrees so that when it goes above that temperature the air conditioner will turn on. What is the input of this system?

PLEASE HELP

Answers

Answer:

Negative Feedback...... Temperature

Explanation:

as the Temperature increase more than the set point the air conditioner turn on to lower the temperature so that means it is Negative feedback because it is not INHANCING the temperature

Input should be Temperature or Heat because AC turns on when the temperature is getting above 70 degrees

NOW WHERE IS MY BRAINLIESTTTT

What occurs during stage one sleep

Answers

Answer:

Stage one of sleep, also known as the transitional phase, occurs when one finds themselves floating in and out of consciousness. During this NREM stage, you may be partially awake while your mind begins to drift off. This period of drowsiness eventually leads to a light sleep

Explanation:

i found it on google

Which particles have more speed: Solid or Liquid? Why?

Answers

Liquid had more speed! Because they are less Densely packed meaning they have more room to gain speed !

Which of the following best explains why engineers are constantly looking for innovative ways to investigate
and improve fluid power designs?
Changes in fluid power systems lead to increased sustainability, such as decreases in fuel costs and carbon emissions.
Changes in fluid power will reach all different types of applications beyond their current uses.
Changes in fluid power will not benefit efficiency ratings but will decrease the costs of products.
Changes are necessary as more designs and products are created and more power systems are required.

Answers

Answer:

Explanation:

What was the answer Im stuck on it rn...

Answer:

Changes in fluid power systems lead to increased sustainability, such as decreases in fuel costs and carbon emissions.

Explanation:

Where is the stigma located?​

Answers

Answer:

At the tip of the pistil

Explanation:

Hope it helped!

A student is moving a magnet through a coil of wire. Which of these indicates the strength of the electric current in the coil?

Answers

Answer:

Can you help me with another question

Explanation:

The electric current in the coil  depends on changes in the magnetic field of the magnet.

Electricity is generated when there is relative motion between a conductor and a magnetic field. As the magnet is being moved through the coil of wire, the magnetic flux around the conductor changes and current is induced on it.

Hence, the strength of the electric current in the coil is determined by  changes in the magnetic field of the magnet.

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How does the organization know what their needs and expectations are ?​

Answers

Answer:

When scientific knowledge changes overtime, it can be to anything at anytime. The Explosion in what we know about life form is important and change because we might have a plant we can’t touch or something like that. That is not the only thing that is important about how scientific knowledge change over time it is also the food pyramid. We know that especially The Explosion in What We Know About Life Forms, is because there might be like a new plant we can’t touch because say it is potions or something. According to the life forms article people are wondering if scientist have found all the living species on earth yet

Explanation:

Condition when an organ is impaired sickness

Answers

Answer:

As traditionally used, impairment refers to a problem with a structure or organ of the body; disability is a functional limitation with regard to a particular activity; and handicap refers to a disadvantage in filling a role in life relative to a peer group.

Explanation:

Hope this helps u

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Sand and salt are poured into a single beaker. The result is a mixture because_____?

Answers

Answer:

Sand and salt are poured into a single beaker. The result is a mixture because they can be separated by simple and easy physical means.

Explanation:

Mixture : Properties :

They are put in a indefinite proportion.They are physically mixed with each other.They can be separated by physical and easily methodsConstituents retain their own properties

Now let us see these in the perspective of the question :

We could have put more of salt and less of sand, still it would not have become a compound. We had poured it into a single beaker with some physical means.We can use sedimentation and evaporation to separate them. After separating them, the will retain their own properties, it is not that the salt will become bitter or the sand will start not allowing the water to flow through it.

These are some few reasons why these getting mixed, becomes a mixture, and we can choose any one point of the properties of mixture and give the answer.

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

5. Use the algebraic technique for adding vectors to find the total displacement of a person who walks the following three paths (displacements-on a flat field. First, she walks 25.0 m in a direction 49.00 north of east. Then she walks 23.0 m heading 15.00 north of east. Finally, she turns and walks 32.0 m in a direction 68.0° south of east. ​

Answers

Answer:

jjjjjjjjjjjjjjjj

Explanation:

A large toy car has a mass of 15 Kg and is pushed horizontally with a force of 2 N. Assume friction is so small it can be ignored. What is the acceleration?

Answers

Answer:

0.133 m/s²

Explanation:

F=ma
F is force
m is mass
a is acceleration


F=ma
2=15.a
a=2/15

a=0.133 m/s²

convert 10 erg into joule​

Answers

Answer:

0.000001

Explanation:

Went to google converter.

What variables do you think affect the strength of the force of gravity between two objects?.

Answers

Answer:

Mass and distance.

Explanation:

The force of gravity is proportional to the masses of the two objects and inversely proportional to the square of the distance between them.

What will make it hard to remember that blood is an organ?
A - it is red
B - it has parts
C - it is a liquid
D - it moves

Answers

Answer:

C . it is a liquid

hope it helps you

QUESTION 4
w
If a car is moving at 37 km/h for 42 min, what is the distance that the car has traveled. (Give your answer in terms of meters and round to
the nearest whole number.)

Answers

Answer:

s=25956m

Explanation:

first 37 km/h is 10.3 m/s

then 42 min is 2520s

finally s=vt => s=2520s*10.3m/s

s=25,956m

Answer:

25956

Explanation:

Convert 37km/h to m/s =10.3m/s

Where s=vt

S=10.3×2520

S=25,956

S=25,000

An athlete needs to get across a river. She must reach from point A on one bank to point B, which is directly across from point A on the opposite bank. If she wishes to minimize the total time T it would take to do so, at what angle upstreams (measured from the line AB) should she swim? Let her swimming/rowing speed relative to the water be 2.0 mi/h, and her running speed along the bank be 5 mi/h. The river flows downstream at 1.5 mi/h. (The rule of the competition stipulates that the athletes must swim first from point A, then run to reach point B.)

Answers

Answer:

θ = 90°

Explanation:

Speed at which she can swim in stationary water; v_m = 2 mi/h

Speed at which the river is flowing downstream; v_r = 1.5 mi/h

This can be illustrated in a form of triangle as attached. Where θ is the angle to the x-axis.

With respect to the bank of the river, the total speed of the girl is;

V_R = v_r + v_m

Now the horizontal component is;

V_R = v_r + v_m(cos θ)

While the vertical component is;

V_R = v_m(sin θ)

Now, the total time taken to get across the river is;

T = width of river/vertical component of total speed

Let's denote width of river as d.

Thus;

T = d/(v_m(sin θ))

Now, we are told she wishes o minimize the total time(T) .

Since the width(d) of the river is constant, and v_m is fixed, then it means the only variable we have is the angle θ.

Now, for the total time to be minimized, the denominator has to be at maximum.

Since angle θ is the only one that is variable, we have to find the value of angle θ that will make sin θ to be at a maximum value.

Now, for sin θ to be maximum, it means it has to be equal to 1.

Thus, θ = sin^(-1) 1

θ = 90°

How can you strengthen the magnetic force of an electromagnet? (check all that apply)

(I'M TAKING TEST PLEASE HELP)

A. Increase the voltage of the battery attached to the electromagnet.

B. Increase the wire coils wrapped around the metal core.

C. Spread out the wire coils wrapped around the metal core.

D. Increase the number of batteries attached to the electromagnet.​

Answers

These are the only 3 ways:

1 wrapping the coil around a piece of iron (such as an iron nail)

2 adding more turns to the coil.

3 increasing the current flowing through the coil.

A boulder of mass 4 kg rolls over a cliff and reaches the beach below with a velocity of 20 metres per second minus 1.

what is the kinetic energy of the boulder when it lands?

what is the potential energy on the cliff?

How high is the cliff??​

Answers

Given:-

Mass of boulder = 10kg

Final Velocity = 15m/s

Acceleration due to gravity = +10m/s

To Find:-

The kinetic energy of the boulder as it lands

The potential energy of the boulder when it was at the top of the cliff

The height of the cliff

Formulae used:-

Kinetic energy = mv²/2

Potential energy = mgh

Now,

We will first find the Kinetic enrgy,

→ K. E = ½mv²

→ K. E = ½ × 10 × (15)²

→ K. E = 5 × 225

→ K. E =1125J

But we know that when the body starts moving the Potential enrgy of the body starts Converting into Kinetic enrgy. Before reaching to the last spot it has equal kinetic energy and Potential energy.

Therefore,

→ mgh = 1125J

The Potential enrgy of the boulder when it was on top is 1125J

Now,

→ mgh = 1125J

→ 10 × 10 × h = 1125J

→ 100h = 1125J

→ h = 1125/100

→ h = 11.25m

Hence, The Height of the Cliff is 11.25m

Thanks!

Mark me brainliest!

what is lighting write its causes​

Answers

Answer: lightning is the occurrence of a natural electrical discharge of very short duration and high voltage between a cloud and the ground or within a cloud, accompanied by a bright flash and typically also thunder.

the causes of lightning:

Lightning happens when the negative charges (electrons) in the bottom of the cloud are attracted to the positive charges (protons) in the ground.

In the early stages of development, air acts as an insulator between the positive and negative charges in the cloud and between the cloud and the ground. When the opposite charges build up enough, this insulating capacity of the air breaks down and there is a rapid discharge of electricity that we know as lightning.

A transformer has 500 volts applied to the primary side and 10,000 volts are measured
on the secondary side. If 10mA is applied to the primary side. What is the anticipated
current on the secondary side? Is this a step-up or step down transformer?

Answers

Answer:

0.5 mA,  step-up transformer

Explanation:

Power is constant

V * I = constant

500 V * 10 mA = 10,000 V * I

so I = 0.5 mA

From 500 V increases to 10,000 V, so it is a step-up transformer

Rihanna can go from 0-60 miles per hour in 3.5 seconds. Calculate the acceleration.
Please show ALL work and CIRCLE your answer.

Answers

Answer:

7.66 m/s²

Explanation:

The following data were obtained from the question:

Initial velocity (u) = 0 mph

Final velocity (v) = 60 mph

Time (t) = 3.5 s

Acceleration (a) =.?

Next, we shall convert mile per hour (mph) to metre per second (m/s). This can be obtained as follow:

Recall:

1 mph = 0.447 m/s

Initial velocity (u) = 0 mph

Initial velocity (u) = 0 × 0.447 = 0 m/s

Final velocity (v) = 60 mph

Final velocity (v) = 60 × 0.447 = 26.82 m/s.

Finally, we shall determine the acceleration of Rihanna as follow:

Initial velocity (u) = 0 m/s

Final velocity (v) = 26.82 m/s.

Time (t) = 3.5 s

Acceleration (a) =.?

a = (v – u) /t

a = (26.82 – 0) / 3.5

a = 26.82 / 3.5

a = 7.66 m/s²

Thus, the acceleration of Rihanna is 7.66 m/s²

Amanda has started running as her primary form of exercise, but she's getting bored with it and finds excuses to procrastinate. It's also getting really hot outside now that it's summer, and Amanda's skin is sensitive to the sun. She has a significant budget available to help her fix the problem but is unsure how to spend the money.

What might be the most appropriate purchase for Amanda?


ANSWER please ⬆️⬆️⬆️ correctly! GIVING OUT BRAINLY STARS!!! ​

Answers

Answer:

: An app thr features menu planning with healthy recipes and pairs with a calorie tracking tool

WHO WANTS BRAINLY? PLEASE ANSWER THIS PHYSICS QUESTION!
force of 187 N acts on a 7.3 kg bowling ball for 0.40 s.
1. What is the change in momentum of the ball?
2. What is its change in velocity?

Answers

Change in momentum of the ball is 74.8 kg m/s

change in velocity of the ball is 0.25 m/s

What is change in momentum?

Change in momentum is the product of mass and change in velocity this is also equal to impusle which ia a product of force and time.

Change in momentum = m ( v - u ) = Impulse = f * t

m = mass

change in velocity = v - u

v = final velocity

u = initial velocity

f = force

t = time

Given:

f  = 187 N

m = 7.3 kg

t = 0.40 s

!.

Change in momentum = impulse = f * t

Change in momentum = 187 * 0.40

Change in momentum = 74.8 kg m/s

2.

Change in momentum = m * ( v - u )

( v - u ) = change in momentum / m

( v - u ) = 187 / 7.3

( v - u ) = 10.25 m/s

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