rileu2661

29.07.2020 • 

Physics

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

Ответ:

lorelei7668

30.01.2022

Physics

---

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 = ρ(r')dA

    Ф = ρ(r')dA

             = 4πα r'dr'

Ф     = 4 π α 1/2(r²-a²)

E(4πr²) = ∈₀

           = ∈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 / 4π∈₀r²

= α / 2 ∈₀ - (α / 2 ∈₀ )(a² / r²) + q / 4 π ∈₀ r²

For  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

---

0,0(0 оценок)

Ответ:

superbatman9193

16.03.2023

Physics

---

Relative to the ground, the ball will be moving with the wagon, accelerating with it, but more slowly than the wagon at first as it rolls back to the rear of the wagon due to inertia and friction. once it is at the rear of the wagon and can't roll back further, it will be seen to accelerate at the same acceleration as the wagon, when viewed relative to the ground. relative to the wagon, the ball will roll back as it will resist change due to inertia when the wagon starts accelerating, due to friction will move in the opposite direction as the wagon, rolling back to the rear.

---

0,0(0 оценок)