Find the electric field E⃗ (r⃗ )E→(r→)E_vec(r_vec) inside the sphere (for rrr< aaa) in terms of the position vector r⃗ r→r_vec. Express your answer in terms of r⃗ r→r_vec, rhorhorho (Greek letter rho), and ϵ0ϵ0epsilon_0.

Answers

Answer 1

Solution :

Using the Gauss law, the electric field intensity of a sphere is given by :

[tex]$E. 4 \pi r^2 = \frac{Q_{enc}}{\epsilon_0}$[/tex]

[tex]$E = \frac{Q_{enc}}{4 \pi r^2 \epsilon_0}$[/tex]

Now the enclosed charge inside the sphere (r<a) is

[tex]$Q_{enc}= \rho V$[/tex]

[tex]$Q_{enc}= \rho \left( \frac{4}{3} \pi r^3 \right)$[/tex]

Hence, the electric field intensity becomes as follows :

[tex]$E= \frac{\rho \left(\frac{4}{3} \pi r^3\right)}{4 \pi \epsilon_0 r^2}$[/tex]

[tex]$E =\frac{\rho r}{3 \epsilon_0}$[/tex]

Thus, the electric field inside the sphere is given by :

[tex]$\vec {E} = \frac{\rho \vec{r}}{3 \epsilon_0}$[/tex]


Related Questions

Can some help me please im confused ‍♀️ !!! I,ll give you BRAINLIES

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Answer:

2 seconds

Explanation:

How would a speed vs. time line graph appear if an airplane moved at a
positive acceleration?

Answers

Answer:

Explanation:

Acceleration is the time rate of change, or the rate, of the velocity. Therefore, the slope y/x of a speed vs time graph would give the acceleration. If the acceleration is said to be positive, the graph would be a straight line that is at a constant increase over time.

What did the Dakota believe about Bdote?

Answers

Answer Bdote means “where two waters come together.” While bdote can refer to any place where waters converge, many Dakota people consider this location as a sacred place of creation, identifying themselves as the Wicahpi  Oyate (Star Nation) who originated in the sky and came into being on this land.

I hope it helpful

What are all of the physics rules?

Answers

Answer:

f this bs

Explanation:

no i will not answer this

Answer: PLEASE GIVE BRIANLIEST

1. Archimedes Principle

2. Avogadro’s Law

3. Ohm's Law

4. Newton’s Laws (1642-1727)

5. Coulomb’s Law (1738-1806)

6. Stefan’s Law (1835-1883)

7. Pascal’s Law (1623-1662)

8. Hooke’s Law (1635-1703)

9. Bernoulli's Principle

10. Boyles's Law

11. Charles's Law

12. Kepler's Law

13. Law of conservation of energy

14. Tyndall effect

15. Graham’s Law

What is a delta?









20 characters...

Answers

Answer:

A river delta is a landform created by deposition of sediment that is carried by a river as the flow leaves its mouth and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, reservoir, or another river that cannot carry away the supplied sediment.

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what is tge scientific teem of the ratio between power out to power in (physics)​

Answers

Answer:

In physics, power is the amount of energy transferred or converted per unit time. In the ... Power (physics) ... Angular acceleration / displacement / frequency / velocity. show. Scientists ... Hence the formula is valid for any general situation. ... because they define the maximum performance of a device in terms of velocity ratios

Explanation:

Most electricity comes from the burning of
A. Fossil fuels B. Trash C. Wood D. None of the above

Answers

Answer:

(A) Fossil Fuels

Answer:

Fossil Fuels

Explanation:

That’s what CK12 told me

Is gravitational energy a form of kinetic energy or potential energy? Why do you think that?

Please help due today!!​

Answers

Answer:

When something is lifted, work is done on the object against the pull of gravity. This work is converted to a form of potential energy called gravitational potential energy. When the item falls towards Earth like an apple from a tree, gravitational potential energy is converted into kinetic energy.

C) If your displacement is 19.3m and your final position is 31.8m, what was your initial position?​

Answers

Answer:12.5

Explanation: Subtract

If an element an atomic number of 32 and a mass of 72, how many neutrons does it have?

Answers

Answer:

41

Explanation:

and your welcome

Which waves can travel through space?

electromagnetic waves only
mechanical waves only
electromagnetic and mechanical waves
longitudinal and electromagnetic waves

Answers

Answer:

Electromagnetic waves only

Only electromagnetic waves can travel through space. hence option A is correct.

What is Electromagnetic waves ?

Electromagnetic waves are the waves associated with photon. Photons carry  electromagnetic waves. it has both electric field and magnetic field perpendicular to each other.

when input of the Dipole antenna is connected to the electric signals having certain frequency. on first half cycle one pole is on positive potential and other is on negative potential. The pole which is at negative potential attracts all the electrons towards it and the pole which is at positive potential attracts positive holes. In the second half cycle polarity of the poles changes and it happen repeatedly, Due to change in polarity of the dipole of the antenna, electrons in the antenna produces electromagnetic waves which we use it for our radio station and mobile phones.

Electromagnetic waves does not require any medium to travel, it can travel through space(vacuum). Waves travels in the medium but there is no medium in the space, but electromagnetic waves are able to travel in the vacuum so scientist named the space as medium of ether.

Hence option A is correct.

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A 2.0 kg rock sits on the edge of a cliff 12 m above the beach. Calculate the kinetic energy of
the rock as it falls off the cliff if the speed of the rock is 15 m/s.

Answers

Answer:

450......

............

Which explanation BEST supports Newton's second law of motion which states that force = mass x acceleration?

Object Y will accelerate the fastest because it has the largest mass.

Object V will accelerate the slowest because it has the smallest mass.

Object Y will require the most force to move because it has the largest mass.

Object V will require the most force to move because it has the smallest mass.​

Answers

The answer is C. F=ma basically says that force is a function of mass multiplied by acceleration. The first two answers don’t make sense because there’s no necessary relationship between mass and acceleration. And for the last two, the higher the mass, the higher the force needed, therefore C is the correct answer.

Which picture is louder?
A) Bottom picture with greater amplitude
B) Top picture with less amplitude

Help me plssss!!!

Answers

Answer:

A

Explanation:

The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound.

Write 4,007,500,000 in scientific notation.
4.0075 x 10 -9 (-9 is an exponent)
4.075 x 10 9 (9 is an exponent)
4007.5 x 10 6 (6 is an exponent)
4.0075 x 10 9 (9 is an exponent)

Answers

The answer is 4.0075 x 10^9

What 2 coins make 30 cents if one of them is not a nickel?

Answers

Answer:

Quarter and Nickel

Explanation:

The speed of the wooden bar is changed so that the bar hits the water fewer times each second.

What happens to the frequency of the waves produced?

A. Increases
B. Does not change
C. Decreases

Answers

Answer:

c - the frequency of the waves decreases

. A hydraulic lift consists of two cylindrical pistons, one with a radius of 1.5 m and
the other with a radius of 8.0 cm. What force must be applied to the smaller piston if
a crate with a mass of 1.5x103 kg is to be raised on the larger piston?
F=42N,

Answers

Answer:

The force that must be applied to the smaller piston if the crate is to be raised by the larger piston is approximately 42 N

Explanation:

The given parameters of the hydraulic lift are;

The diameter of one of the pistons = 1.5 m

The diameter of the other pistons = 8.0 cm = 0.08 m

The mass of the crate to be lifted with the larger piston, m = 1.5 × 10³ kg

The weight of the mass to be lifted by the larger piston, W₁ = m × g

Where;

g = The acceleration due to gravity = 9.8 m/s²

Therefore;

W₁ = 1.5 × 10³ kg × 9.8 m/s² = 14,700 N

The area of the surface of the circular piston, A = π × r²

Where;

r = The piston's radius

∴ The area of the larger piston with 1.5 m radius, A₁ = π × (1.5 m)² = 7.06868347058 m² ≈ 7.07 m²

A₁ ≈ 7.07 m²

The area of the smaller piston with 0.08 m (8 cm) radius, A₂ = π × (0.08 m)² = 02010619298 m² ≈ 0.02 m²

A₂ ≈ 0.02 m²

The pressure in the fluid of the hydraulic lift is constant, therefore, we have;

The pressure applied to the larger piston with 1.5 m radius, P₁ = The pressure applied to the smaller piston with 0.08 m radius, P₂

∴ P₁ = P₂

[tex]Pressure = \dfrac{Force}{Area}[/tex]

[tex]P_1 = \dfrac{W_1}{A_1} = \ P_2 = \dfrac{F_2}{A_2}[/tex]

[tex]\therefore \dfrac{W_1}{A_1} = \ \dfrac{F_2}{A_2}[/tex]

Where, F₂, represents the force that must be applied to the smaller piston if the crate is to be raised by the larger piston;

[tex]\therefore F_2 = A_2 \times \dfrac{W_1}{A_1}[/tex]

Given that we have the ratio of two areas which have π as a factor, we have;

[tex]\therefore F_2 = A_2 \times \dfrac{W_1}{A_1} = 0.08^2 \times \pi \times \dfrac{14,700}{1.5^2 \times \pi } = 41.81 \overline 3[/tex]

The force that must be applied to the smaller piston if the crate is to be raised by the larger piston, F₂ = 41.81[tex]\overline 3[/tex] N ≈ 42 N.

What is the independent variable?

Diameter
Circumference

Answers

Answer:

Diameter

Explanation:

I know that circumference is dependent, so diameter has to be independent

The circumference is dependent, so diameter has to be independent.

What are independent variables?

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.

Diameter is the line from one point in the circle to the other point through the center of the circle.

The circumference of the circle that has a radius of r is the product of diameter to the pie value.

The circumference is dependent, so diameter has to be independent.

Learn more about independent variable;

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I NEED HELP ASAP!!!!!!!
A balloon has a volume of 25.0 L at a pressure of 98.7 kPa. Will the new volume be more or less that 25.0 L whe
the pressure is 51.2 kPa?

Answers

Answer:

It will be more

Explanation:

Pressure and volume relationships between gases is given by the Boyle's law.

According to this law, we know that:

  "the volume of a fixed mass of a gas varies inversely as the pressure changes if the the temperature is constant".

So, the higher the pressure on a body, the lower it's volume and vice versa.

Since we set off at a higher pressure and wants to end at a lower pressure, the volume of the gas will increase more.

Is this right? Please help me

Answers

Answer:

It would be C

Explanation:

The brain operates on two levels, one of them is unconscious.

This would be definitely C

A car travels for a time of 2.4 hours at a speed of 65Km/hr. How far has it traveled?

Answers

Answer: 27.1 km

Explanation:

Divide 65km/h and 2.4hr

For a complete vector quantity, what information needs to be given?

Answers

The magnitude of the quantity and its direction.

Earth's rotation causes winds to veer to the west or to the east. This is known as the Coriolis effect.

Lesson 1.06



Question 5 options:
True
False

Answers

Earth's rotation and spherical shape cause winds to veer to the right (in the northern Hemisphere) or to the left (in the southern Hemisphere) of the direction they want to go.  This is known as the Coriolis effect.

If you didn't know that you're on a rotating Earth, and you looked at the patterns of the winds, you'd think there's some kind of force that's making the airflow veer to the right or left of the direction it actually wants to go.  This is known as the Coriolis force.  It's a"pseudo force", because it doesn't really exist.  It only LOOKS like it's there, because of the Earth's rotation and spherical shape..

The statement "Earth's rotation causes winds to veer to the west or to the east" is true about the Coriolis effect.

What is the Coriolis effect?

Fluid materials such as wind and ocean currents take different directions depending on the hemisphere, this movement of deviation is called the Coriolis effect.

Characteristics of the Coriolis effect

The Coriolis effect occurs when masses of air or water move along terrestrial meridians, and their trajectory and speed are modified by it.

The winds or ocean currents that move along a meridian are diverted by accelerating in the direction of rotation (east) if they go towards the poles or the opposite (west) if they go towards the equator.

Therefore, we can conclude that the force that tends to deflect the trajectory of objects moving across the entire earth's surface is known as the Coriolis effect.

Learn more about the Coriolis effect here: https://brainly.com/question/14290551

As a gas or liquid increases in heat, what direction will it naturally move?

Answers

Hello!

Answer:

When a gas gets hot it should go up because of the pressure.

Explanation:

Hope this helps!

Some chemical reactions release energy. Others store energy. What important chemical reaction stores energy?

Answers

Chemical energy energy stored in the bonds of chemical compounds. Chemical energy maybe realized during a chemical reaction of in the form of heat

I'll mark as brainliest if your answer is correct!!

#1: A study performed yielded results that indicated the more natural sunlight a person was exposed to, the more likely they were to show increases in serotonin in their bloodstreams. This correlation is an example of a _______ correlation.



#2: researchers were interested to see how many people who break the speed limit could be deterred from their bad behavior. Upon observation,they noticed that the more often and frequent law enforcement appeared at Highway stops the less likely people were to speed in that area. This correlation is a great example of a ____ correlation.

Answers

1. positive correlation
2. negative correlation
Hi can you help me and I’ll help you

As a gas or liquid decreases in heat (gets cooler), what direction will it naturally move?

Answers

it should go up because of the pressure

1. If an object starts at 0 m/s and 0.0001 seconds later the object is travelling at
400 m/s what is the objects acceleration?

Answers

Answer:

4 x 10⁶m/s²

Explanation:

Given parameters:

Initial velocity  = 0m/s

Time  = 0.0001s

Final velocity  = 400m/s

Unknown:

Acceleration of the object  = ?

Solution:

Acceleration is the rate of change of velocity with time;

 Acceleration  = [tex]\frac{Final velocity - Initial velocity }{Time }[/tex]  

 Acceleration  = [tex]\frac{400 - 0}{0.0001}[/tex]   = 4 x 10⁶m/s²

help me!
Bill left a hammer out in the rain all day. The next morning it had rust on it.
Oxygen and a metal chemically combine to form rust. What is rust an example of?
O a mixture
• a solution
an element
a compound

Answers

It is a compound yep

Answer:D.Compound

Explanation: internet

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