Answer:
62.8 μC
Explanation:
Here is the complete question
The volume electric charge density of a solid sphere is given by the following equation: ρ = (0.2 mC/m⁵)r²The variable r denotes the distance from the center of the sphere, in spherical coordinates. What is the net electric charge (in μC) of the sphere if the radius of the sphere is 0.5 m?
Solution
The total charge on the sphere Q = ∫∫∫ρdV where ρ = volume charge density = 0.2r² and dV = volume element in spherical coordinates = r²sinθdθdrdΦ
So, Q = ∫∫∫ρdV
Q = ∫∫∫ρr²sinθdθdrdΦ
Q = ∫∫∫(0.2r²)r²sinθdθdrdΦ
Q = ∫∫∫0.2r⁴sinθdθdrdΦ
We integrate from r = 0 to r = 0.5 m, θ = 0 to π and Φ = 0 to 2π
So, Q = ∫∫∫0.2r⁴sinθdθdrdΦ
Q = ∫∫∫0.2r⁴[∫sinθdθ]drdΦ
Q = ∫∫0.2r⁴[-cosθ]drdΦ
Q = ∫∫0.2r⁴-[cosπ - cos0]drdΦ
Q = ∫∫∫0.2r⁴-[-1 - 1]drdΦ
Q = ∫∫0.2r⁴-[- 2]drdΦ
Q = ∫∫0.2r⁴(2)drdΦ
Q = ∫∫0.4r⁴drdΦ
Q = ∫0.4r⁴dr∫dΦ
Q = ∫0.4r⁴dr[Φ]
Q = ∫0.4r⁴dr[2π - 0]
Q = ∫0.4r⁴dr[2π]
Q = ∫0.8πr⁴dr
Q = 0.8π∫r⁴dr
Q = 0.8π[r⁵/5]
Q = 0.8π[(0.5 m)⁵/5 - (0 m)⁵/5]
Q = 0.8π[0.125 m⁵/5 - 0 m⁵/5]
Q = 0.8π[0.025 m⁵ - 0 m⁵]
Q = 0.8π[0.025 m⁵]
Q = (0.02π mC/m⁵) m⁵
Q = 0.0628 mC
Q = 0.0628 × 10⁻³ C
Q = 62.8 × 10⁻³ × 10⁻³ C
Q = 62.8 × 10⁻⁶ C
Q = 62.8 μC
They both provide a range of years of an object. I think. They’re just 2 different ways to tell the age of fossils or rocks
The characteristics of the velocity vector used to find the results for the direction of acceleration and velocity are:
- Acceleration is towards the center of the circle
- The velocity is tangent to the circle counterclockwise.
Newton's Second Law establishes a relationship between force, mass and acceleration of bodies.
<h3>Centripetal acceleration.
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In the case of circular motion there is a constant change in the direction of the velocity vector, even when its module remains constant, this change in direction points towards the center of the circle, so that the module is constant.
They indicate that the satellite is moving counterclockwise, therefore the speed must go to the left (counterclockwise) tangential to the circle.
In conclusion using the characteristics of the velocity vector we can find the results for the direction of acceleration and velocity are:
- Acceleration is towards the center of the circle
- The velocity is tangent to the circle counterclockwise.
Learn more about centripetal acceleration here: brainly.com/question/25243603
Magic magic and more magic
Answer:
Beats are the difference in frequency.
(a) is correct option.
Explanation:
Beat :
Beat is the difference of the frequency of two waves.
The difference in frequency is equal to the number of beat per second.
Amplitude :
Amplitude of the wave is the maximum displacement.
Frequency :
Frequency is the number oscillations of wave in per second.
Intensity :
Intensity is the power per unit area.
Hence, Beats are the difference in frequency.
