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
Answer:
Convection is the transfer of heat from one place to another along with the motion of the object's particles. Water is a poor conductor. However, when the bottom water is heated, it turns out that the top water is also hot. This means that there is another way of transferring heat to the water, namely convection.
Oil is made from buried remains of plants and animals.
<span>A.
Gravitational force is proportional to the square of the distance
between the centers of both bodies.
FALSE:
Gravitational force is inversely proportional to the square of the distance between the centers of both bodies.
Which you can see from the formula: F = G * [m*M] /(d^2)
As you see in the equation, d^2 is in the denominator so the bigger d^2 (the square of the distance between the centers) of the objects the smaller the gravitational force.
B. The object with the smaller mass
does most of the moving because the object with the larger mass has too
much inertia to move any noticeable amount.
TRUE:
F = mass * acceleration => acceleration = F / mass => the larger the mass the smaller the acceleration.
C. Gravitational force is
proportional to the product of the two masses.
TRUE:
F = G [m*M] / (d^2)
The product of the two masses, m*M, is in the numerator, so F is proportional to this product.
D. Every object in the
universe that has mass attracts every other object in the universe that
has mass.
TRUE: that is a Universal Law discovered by Sir Isaac Newton.
</span>
Earth science, A would be the answer!
