Answer:
E_total = 5.8 10⁴ N /C
Explanation:
In this problem they ask to find the electric field at two points, the electric field is a vector magnitude, so we can find the field for each charged shoah and add them vectorally at the point of interest.
To find the electric field of a charged conductive sheet, we can use the Gauss law,
Ф = E. d S = / ε₀
Let us use as a Gaussian surface a small cylinder, with the base parallel to the sheet, the electric field between the sheet and the normal one next to the cylinder has 90º, so its scalar product is zero, the electric field between the sheet and the base has An Angle of 0º, therefore the scalar product is reduced to the algebraic product.
Let's look for the electric field for plate 1
The total flow is the same for each face, as there are two sides of the cylinder
2E A = q_{int} /ε₀
For the internal load we use the concept of surface density
σ = q_{int1} / A
q_{int1} = σ₁ A
Let's replace
2E A = σ₁ A /ε₀
E₁ = σ₁ / 2ε₀
For the other plate we have a field with a similar expression, but of negative sign
E₂ = -σ₂ / 2ε₀
The total field is,
E_total = σ₁ / 2ε₀ + σ₂ / 2ε₀
E_total = (σ₁ + σ₂) / 2ε₀
Let us apply this expression to our case, when placing a sheet without electric charge, a charge is induced for each sheet, the plate 1 that has a positive charge the electric field is protruding to the right and the plate 2 that has a negative charge creates a incoming field, to the right, as the two fields have the same address add
The conductive sheet in the middle pate undergoes an induced load that is created by the other two plates, but because the conductive plate the charges are mobile and are replaced.
E_total = (0.51 +0.52) 10⁻⁶ / 2 8.85 10⁻¹²
E_total = 5.8 10⁴ N /C
Note that the field is independent of the distance between the plates
Answer:
Explanation:
First of all, we need to find the pressure exerted on the sphere, which is given by:
where
is the atmospheric pressure
is the water density
is the gravitational acceleration
is the depth
Substituting,
The radius of the sphere is r = d/2= 1.1 m/2= 0.55 m
So the total area of the sphere is
And so, the inward force exerted on it is
1) 26.2 m/s
The mechanical energy of the divers at any point of their vertical motion is sum of the kinetic energy and the gravitational potential energy:
where
m is the mass of the diver
v is the speed
g = 9.8 m/s^2 is the acceleration due to gravity
h is the height above the water
When the diver is on the cliff, v = 0 (he is at rest), so K=0 and the initial mechanical energy is just potential energy:
where h=35 m is the height of the cliff.
When the diver hits the water above, h = 0, so U=0 and the final mechanical energy is just kinetic energy:
since the total mechanical energy is conserved, we have
And solving the equation for v, we find the speed when they reach the surface of the water:
2) It is converted into thermal energy of the water
When the diver enters the water, he suddenly feels another force acting against the motion of the diver: the resistance of the water. The resistance of the water acts upward, slowing down the diver until he stops.
In this process, the speed of the diver (v) decreases, and therefore the kinetic energy of the diver decreases as well, until it becomes zero.
However, this does not mean that the conservation of energy has been violated. In fact, the kinetic energy of the diver has been converted into thermal energy of the molecules of water surrounding the diver.