Answer:
Explanation:
Electric field E = 4 x 10⁷ V / m
Dielectric constant k = 24
capacitance of capacitor
C = kε₀ A / d
d = plate separation
A = plate area
C = .89 x 10⁻⁶
V / d = electric field
for minimum d , electric field will be maximum
V / d = 4 x 10⁷
1930 / d = 4 x 10⁷
d = 1930 / 4 x 10⁷
d = 482.5 x 10⁻⁷ m
= 48.25 x 10⁻⁶ m
C = kε₀ A / d
.89 x 10⁻⁶ = 24 ε₀ A / d
A = .89 x 10⁻⁶ X d / 24 ε₀
A = .89 x 10⁻⁶ X 48.25 x 10⁻⁶ / 24 x 8.85 x 10⁻¹²
= 42.9 / 212.4
= .2019 m²
The concept required to solve this problem is linked to inductance. This can be defined as the product between the permeability in free space by the number of turns squared by the area over the length. Recall that Inductance is defined as the opposition of a conductive element to changes in the current flowing through it. Mathematically it can be described as
Here,
= Permeability at free space
N = Number of loops
A = Cross-sectional Area
l = Length
Replacing with our values we have,
Therefore the Inductance is
a) 1.57 m/s
The sock spins once every 2.0 seconds, so its period is
T = 2.0 s
Therefore, the angular velocity of the sock is
The linear speed of the sock is given by
where
is the angular velocity
r = 0.50 m is the radius of the circular path of the sock
Substituting, we find:
B) Faster
In this case, the drum is twice as wide, so the new radius of the circular path of the sock is twice the previous one:
At the same time, the drum spins at the same frequency as before, therefore the angular frequency as not changed:
Therefore, the new linear speed would be:
And substituting,
So, we see that the linear speed has doubled.
Answer:
The depth is 5.15 m.
Explanation:
Lets take the depth of the pool = h m
The atmospheric pressure ,P = 101235 N/m²
The area of the top = A m²
The area of the bottom = a m²
Given that A= 1.5 a
The force on the top of the pool = P A
The total pressure on the bottom = P + ρ g h
ρ =Density of the water = 1000 kg/m³
The total pressure at the bottom of the pool = (P + ρ g h) a
The bottom and the top force is same
(P + ρ g h) a = P A
P a +ρ g h a = P A
ρ g h a = P A - P a
h=5.15 m
The depth is 5.15 m.