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

please help! you are amazing! brainliest too!

NASA helps fund science education.

Which statement about scientific knowledge is false?

A. Understanding science can help people make wiser purchases.
B. People with more knowledge of science are always healthier.
C. People with college degrees in science often earn high salaries.
D. Science education can help people understand the universe.

Answers

I think it’s B hope it helps:)

Answer:

I think its B and I don't know why my words are like this

Explanation:

a girl pushes her little brother down a snowy hill on a sled and he rides quickly to the bottom of the hill

which one of Newton's Laws is this ​

Answers

Answer:

Newton's First Law of Motion.

Explanation:

Inertia can be defined as the tendency of an object or a body to continue in its state of motion or remain at rest unless acted upon by an external force.

In physics, Sir Isaac Newton's First Law of Motion is known as law of inertia and it states that, an object or a physical body in motion will continue in its state of motion at continuous velocity (the same speed and direction) or, if at rest, will remain at rest unless acted upon by an external force.

In this scenario, a girl pushes her little brother down a snowy hill on a sled and he rides quickly to the bottom of the hill. The push from the little boy's sister is the external force acting on him and consequently, causing him to be in motion down the snowy hill.

A highway speed limit is posted as 90 km/hr. Is this average speed or instantaneous speed? Explain your answer.

Answers

Answer: instantaneous speed.

Explanation: A highway speed limit posted as 90km/hr would be the instantaneous speed because it’s just the speed for that moment.

Romeo traveled by a 900 kg horse from Manitua to Verona accelerating at the rate of 20 km/hr. With what force is Romeo moving at?

Answers

Answer:

Force(Romeo moving) = 5,000 N

Explanation:

Given:

Mass of horse = 900 kg

Acceleration = 20 km/hr

Find:

Force(Romeo moving)

Computation:

Acceleration = 20 km/hr

Acceleration in m/s = 20 / 3.6 = 5.555556 m/s²

Force = m x a

Force(Romeo moving) = 900 x 5.555556

Force(Romeo moving) = 5,000 N

While driving his sports car at 20.0 m/s through a residential neighborhood, Royston
comes up behind a slow-moving grandma and decides to pass her on the left. If
Royston can accelerate at 6.00 m/s2, how long will it take for him to reach a velocity of
30.0 m/s?

Answers

Answer:

1.67s

Explanation:

Given parameters:

Initial velocity  =  20m/s

Acceleration  = 6m/s²

Final velocity  = 30m/s

Unknown:

Time taken  = ?

Solution:

Acceleration is the rate of change of velocity with time. It is mathematically expressed as;

 Acceleration = [tex]\frac{v - u }{t}[/tex]  

v is the final velocity

u is the initial velocity

 t is the time taken

            6  =[tex]\frac{30 - 20}{t}[/tex]  

            6  = [tex]\frac{10}{t}[/tex]  

              10  = 6t

              t  = 1.67s

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 car has a mass of 1500 kg and accelerates at a rate of 15 m/s^. What was the force applied?

Answers

Answer:

22500N

Explanation:

Given parameters:

Mass of the car  = 1500kg

Acceleration  = 15m/s²

Unknown:

Force applied  = ?

Solution:

From Newton's second law of motion:

  Force  = mass x acceleration

So

     Force  = 1500 x 15  = 22500N

Explain how are position time, velocity, and acceleration related to each
other?

Answers

I had this question before I think was it A or B.

An object of mass m is placed on Spring A, which is compressed by distance x. The spring is released and the velocity of the pushed object as it leaves the spring is measured. The experiment is repeated with the same object on Spring B, which is compressed by the same distance x. The object travels faster when pushed by Spring B. What can be concluded?

A .Spring A had a higher elastic potential energy than Spring B.
B. Spring A's spring constant is higher than Spring B's.
C. Spring A's spring constant is lower than Spring B's.
D. Spring A has more mass than Spring B.

Answers

Answer:

C

Explanation:

Other Questions
All of the following are used to describe relative location except:a.Distance between placesb.Latitude and longitude coordinatesc.Landmarksd.Direction please help solve this, i can't figure out how to do it Define the meaning of Sparta's governing bodies:Appeals:Gerussia: Eforato: the graph shows the voltage in a circuit changing as temperature increases from 100 to 600. which is the best estimate for the rate of change of the voltage over the interval?1.5 volts3 5 volts5.5 volts7.5 volts You pay $11.20 to buy drink boxes for the football team. Each drink box cost $0.40. How many drink boxes didyou buy? 3(9+c+b) if c=13 and b=4 During which of the following time periods did the supercontinent Pangaea split into two blocks, Laurasia and Gondwanaland?A) CarboniferousB) CambrianC) PermianD) Tertiary HURRY PLS CAN SOMEONE PLEASE HELP ME In one or two paragraphs, explain how the Nile River influenced the relationship between Egypt and Nubia. How did it encourage similarities in Egyptian and Nubian culture? How did it also create cultural differences? Whats the anwser for this. Im so confused how do u say there is one flag located above the trash can in spanish Who is the 1st president What posture is a dog displaying if she is leaning away from your, body lowered, ears back, tail down, showing whites of her eyes and the corners of her mouth pulled back. A spring has a constant of 875 N/m. What hanging mass will cause this spring to stretch 4.5 m? What is mDEF?Enter your answer in the box. There is a triangle DEF in which side DE is congruent to side EF and G is the midpoint of the side DF. Segment EG intersect the side DF at point G. The measure of angle DEG is (3y+4) degrees and the measure of angle FEG is (5y-10) degrees. If you understand spanish can you help me-ive tried doing it but i still don't understand it Slope of -1 through point (3,-1) Write a java program named BMI.java(i)print out your name and your pantherID(ii) Ask user to type in his/her weight and height; if an illegal input (such as a letter) is typed by the user, give the user one more chance to input correctly.(iii)Create a method to compute the body mass index (BMI) accordingly. BMI We have a bilateral triangle with base length 2 and sidelengths x where x is increasing at a rateof 5 units per minute.Find the rate of change of the side angle teta when x=2. please help fast im timed Which sentence best introduces a claim about character motivation in Shakespeare's Julius Caesar?A. In the play Julius Caesar, Brutus is conflicted between staying loyal to Caesar or loyal to Rome.B. In the play Julius Caesar, Shakespeare includes many characters with motivations.C. In the play Julius Caesar, Brutus is part of a plot to conspire against Caesar.D. In the play Julius Caesar, Shakespeare shows the impact of Caesars death on the Roman government. Find the mid segment of GH