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ELEN [110]
3 years ago
13

A solid uniformly charged insulating sphere has uniform volume charge density p and radius R. Apply Gauss's law to determine an

expression for the magnitude of the electric field at an arbitrary distance r from the center of the sphere, such that r < R, in terms of rho and r
Physics
1 answer:
RUDIKE [14]3 years ago
4 0

Answer:

electric field E = (1 /3 e₀) ρ r

Explanation:

For the application of the law of Gauss we must build a surface with a simple symmetry, in this case we build a spherical surface within the charged sphere and analyze the amount of charge by this surface.

The charge within our surface is

 

     ρ = Q / V

     Q ’= ρ V '

The volume of the sphere is V = 4/3 π r³

     Q ’= ρ 4/3 π r³

The symmetry of the sphere gives us which field is perpendicular to the surface, so the integral is reduced to the value of the electric field by the area

      I E da = Q ’/ ε₀

      E A = E 4 πi r² = Q ’/ ε₀

      E = (1/4 π ε₀) Q ’/ r²

Now you relate the fraction of load Q ’with the total load, for this we use that the density is constant

     

      R = Q ’/ V’ = Q / V

How you want the solution depending on the density (ρ) and the inner radius  (r)

      Q ’= R V’

      Q ’= ρ 4/3 π r³

      E = (1 /4π ε₀) (1 /r²) ρ 4/3 π r³

     E = (1 /3 e₀) ρ r

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Now the elevator is moving downward with a velocity of v = -2.8 m/s but accelerating upward with an acceleration of a = 5.5 m/s2
borishaifa [10]

Answer:

160.75 N

Explanation:

The downward velocity has no effect on the force situation, it is only changes in velocity (plus, of course, gravity, which is always there) that require a force. At constant velocity, the bottom spring s_3 is supporting its mass m_3 to balance gravity.

As the elevator slows, though, it also ends up slowing down the spring arrangement, too. However, because the stretching takes time, it means that some damped harmonic motion will be set up in the spring chain.

When the motion has finally damped out, the net force the bottom spring s3 exerts on m3 has two components--that of gravity and of the deceleration of the elevator:

F_3net = m3 * (g + a) = 10.5×(9.81+5.5)= 10.5×15.31= 160.75 N

5 0
3 years ago
What are forces that two objects apply on each other
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3 0
3 years ago
A woman is 160160cm tall. What is the minimum vertical length of a mirror in which she can see her entire body while standing up
kipiarov [429]

This question is incomplete, the complete question is;

A woman is 160cm tall. What is the minimum vertical length of a mirror in which she can see her entire body while standing upright.

Hint: Consider the ray diagram below, of the rays that enable her to see her feet and the top of her head.

Use what you know about the law of reflection, together with a bit geometry.

The missing Image is uploaded along this answer below.

Answer:

the minimum vertical length of a mirror in which she can see her entire body while standing upright is 80 cm

Explanation:

Given the data in the question and illustrated in the image below,

From image 2;

The distance from the woman's eyes to the top of her head is represented as b and a represent the distance from her eyes to her feet.

Therefore, since her height is 160 cm

a + b = 160 ------ let this be equation 1

i.e AD + DG = 160 cm

Now, from the same image 2, we will notice that triangle ABC and tringle CBD are similar, so

∠ABC = ∠CBD

AC = CD

since AD = a and AC + CD = A

AC = CD = a/2

Also, triangle DEF and FEG are si,ilar

∠DEF = ∠FEG

so

DF = FG

since DG = b and DF + FG = b

DF = b/2

so the minimum vertical length of a mirror in which the woman can see her entire body while standing upright will be;

⇒ a/2 + b/2  

⇒ a + b / 2

from equation 1, a + b = 160

so

⇒ a + b / 2 = 160 / 2 = 80

Therefore, the minimum vertical length of a mirror in which she can see her entire body while standing upright is 80 cm

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Fynjy0 [20]
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