Answer:
Explanation:
Given that,
Radius r = 15cm = 0.15m
Area of the circular loop can be determined using the formula for area of a circle
A = π r²
A = π × 0.15²
A = 0.0708 m²
Magnetic field B = 1.2T in positive z direction
B = 1.2 •k T.
If loop is remove from the field in the time interval
∆t = 2.3ms = 2.3×10^-3s
We want to find the average EMF and it is given as
ε = —∆Φ/∆t
The final flux is zero
Φf = 0
Where magnetic flux is given as
Φi = BA Cosθ
Where θ=0 since the area and the magnetic field point in the same direction.
Φi = BA Cos0
Φi = BA
Φi = 1.2 × 0.0708
Φi = 0.0848 Vs
Then, ε = —∆Φ/∆t
ε = —(Φf — Φi) / ∆t
ε = —(0-0.0848) / (2.3×10^-3)
ε = 0.0848 / (2.3×10^-3)
ε = 36.88 V
The EMF is 36.88 Volts
Here is the full question
Suppose there are 10,000 civilizations in the Milky Way Galaxy. If the civilizations were randomly distributed throughout the disk of the galaxy, about how far (on average) would it be to the nearest civilization?
(Hint: Start by finding the area of the Milky Way's disk, assuming that it is circular and 100,000 light-years in diameter. Then find the average area per civilization, and use the distance across this area to estimate the distance between civilizations.)
Answer:
1000 light-years (ly)
Explanation:
If we go by the hint; The area of the disk can be expressed as:

where D = 100, 000 ly
Let's divide the Area by the number of civilization; if we do that ; we will be able to get 'n' disk that is randomly distributed; so ;

The distance between each disk is further calculated by finding the radius of the density which is shown as follows:



replacing d =
in the equation above; we have:




The distance (s) between each civilization = 
= 2 (500 ly)
= 1000 light-years (ly)
Define
v = volume of a drop per second, cm³/s
The time taken to fill 200 cm³ is 1 hour.
Let V = 200 cm³, the filled volume.
Let t = 1 h = 3600 s, the time required to fill the volume.
Therefore,

The average volume of a single drop is approximately 0.0556 cm³.
Answer: 0.0556 cm³