1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Charra [1.4K]
3 years ago
11

An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is g

iven by rho(r)=αr,where α is a positive constant.
A). What is the magnitude of the electric field at a distance r from the center of the shell, where a Express your answer in terms of the variables α, a, r, and electric constant ϵ0.
B) .A point charge
q is placed at the center of the hollow space, at r=0. What value must q have (sign and magnitude) in order for the electric field to be constant in the region a Express your answer in terms of the variables α, a, and appropriate constants.
C). What then is the value of the constant field in this region?
Express your answer in terms of the variable αand electric constant ϵ0.
Physics
1 answer:
allsm [11]3 years ago
4 0

Answer:

E   = α/2∈₀ [ 1 - a²/r² ]

Ф = α/2∈₀

Explanation:

Using Gauss Law:

    ρ(r) = a/r, dA

          = 4 π r²d r

    Ф = \int\limits^r_a ρ(r')dA

    Ф_{encl} = \int\limits^r_a ρ(r')dA

             = 4πα \int\limits^r_a r'dr'

Ф_{encl}     = 4 π α 1/2(r²-a²)

E(4πr²) = 2\pi\alpha  (r^{2}-a^{2}  )/∈₀

           = 2\pi\alpha  (r^{2}-a^{2}  )/∈₀(4πr²)

           = α (r² - a²) / 2 ∈₀ (r²)

           = α/2∈₀ [ r²/r² - a²/r² ]

      E   = α/2∈₀ [ 1 - a²/r² ]

Electric field of the point charge:

E_{q} = q / 4π∈₀r²

E_{total} = α / 2 ∈₀ - (α / 2 ∈₀ )(a² / r²) + q / 4 π ∈₀ r²

For E_{total}  to be constant:

- (αa²/ 2 ∈₀ ) + q / 4 π ∈₀ = 0 and q = 2παa²

-> α / 2 ∈₀ - αa²/ 2 ∈₀ + 2παa² / 4 π ∈₀

= α - αa² + αa² / 2 ∈₀

= α /2 ∈₀

Hence:

Ф = α/2∈₀

You might be interested in
A block is thrown with an initial velocity of 30.0 m/s at an angle of 25.0o above the horizontal. What is the highest elevation
Serga [27]

The highest elevation reached by the ball in its trajectory is 16.4 m.

To find the answer, we need to know about the maximum height reached in a projectile.

What's the mathematical expression of the maximum height reached in a projectile motion?

  • The maximum height= U²× sin²(θ)/g
  • U= initial velocity, θ= angle of projectile with horizontal and g= acceleration due to gravity

What's the maximum height reached by a block that is thrown with an initial velocity of 30.0 m/s at an angle of 25° above the horizontal?

  • Here, U = 30.0 m/s and θ= 25°
  • Maximum height= 30²× sin²(25)/9.8

= 16.4m

Thus, we can conclude that the highest elevation reached by the ball in its trajectory is 16.4 m.

Learn more about the projectile motion here:

brainly.com/question/24216590

#SPJ4

3 0
2 years ago
A tectonic plate is part of the Earth’s lithospherehttp://brainly.com/question/add?entry=1642&task_content=A%20tectonic%20pl
lord [1]
Plate tectonics<span>is a </span>scientific theory<span> that describes the large-scale motion of </span>Earth<span>'s </span>lithosphere<span>. This theoretical model builds on the concept of </span>continental drift<span> which was developed during the first few decades of the 20th century. The </span>geoscientific<span> community accepted plate-tectonic theory after </span>seafloor spreading was validated in the late 1950s and early 1960s.<span>The lithosphere, which is the rigid outermost shell of a planet (the crust and upper mantle), is broken up into </span>tectonic plates<span>. </span>
3 0
3 years ago
If an astronaut can throw a certain wrench 15.0 m vertically upward on earth, how high could he throw it on our moon if he gives
Sever21 [200]

Answer:

hm= 18.2 m

Explanation:

Solution is attached

5 0
3 years ago
Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement co
dalvyx [7]

Answer:

Its acceleration is positive

Explanation:

As the car is moving in the negative x-direction than after applying brake then there will be a decrease in the acceleration but in the opposite direction.

As decreasing acceleration consider to be negative but the car is moving in negative direction which means increasing acceleration is negative by sign convention but by applying brake acceleration decrease but in opposite direction than it will give positive value of acceleration.

4 0
3 years ago
What is the value of work done on an object when a 70-newton force moves it 9.0 meters in the same direction as the force?
marta [7]
630 watts - 9 x 70 = 630
4 0
3 years ago
Read 2 more answers
Other questions:
  • The conductive tissues of the upper leg can be modeled as a 40-cm-long, 12-cm-diameter cylinder of muscle and fat. The resistivi
    8·1 answer
  • When current increases and resistance remains constant what happens to voltage?
    6·1 answer
  • If we approximate the rack to be completely flat and the racecar is travelling a constant 30.5 m/s around the turn, what forces
    14·1 answer
  • Suppose that you release a small ball from rest at a depth of 0.730 m below the surface in a pool of water. If the density of th
    11·1 answer
  • Which of the following statements about the resistsance of a wire is correct? Select THREE answers.
    11·1 answer
  • The electric field strength E is measured as:
    11·1 answer
  • An airplane crooses the United States from San Francisco to Boston in 4 hours 20 min. Find the average speed if the distance is
    8·1 answer
  • What do you meant by varnier constant?
    12·1 answer
  • All objects in our solar system orbit the Sun. How is the movement of planets like
    12·1 answer
  • What is random motion? write any two examples​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!