What do we mean by the event horizon of a black hole?
2 answers:
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Answer:
1) E = 0 , 2) zero, 3) E = - 2,162 10⁴ N/C , 4) directed towards the center of the sphere , 5) E = 1.412 10⁴ N / C , 6)direction coming out of the sphere
Explanation:
The electric field is a vector quantity, therefore we can calculate the field due to each charge distribution and add vector
E = E₁ + E₂
To calculate each field we can use Gauss's law, which states that the flow is equal to the charge by the Gaussian surface divided by ε₀
For this case, let's take a sphere as a Gaussian surface
Ф = ∫E dA = /ε₀
The area of a sphere is
A = 4π r²
E = 1 / 4πε₀ q_{int} / r²
1) r = 4 cm
This radius is smaller than the radius of the sphere, therefore the charge inside is zero and therefore the field is zero
E = 0
2) there is no field
3) r = 8 cm
Let's calculate each field, for the inner surface
This radius is larger than the internal radius, so the field is
σ = q_{int} / A
The area of the sphere is
V = 4 π R_in²
Rho = q_{int} / 4π R_in²
q_{int} = ρ 4π R_in²
E₁ = 1 /ε₀ ρ r_in² / r²
For the outer surface
This radius is smaller so there is no load inside the Gaussian surface and therefore the field is zero
E₂ = 0
Total E
E = E₁ + 0
E = 1 /ε₀ ρ₁ R_in² / r²
Let's calculate
E = 1 /8,854 10⁻¹² 250 10⁻⁹ (7/8)²
E = - 2,162 10⁴ N / C
4) as the electric field is negative, it is directed towards the center of the sphere
5) r = 12 cm
In this case the two surfaces contribute to the electric field,
Inner surface
Q₁ = ρ₁ 4π R_in²
E₁ = 1 /ε₀ ₁rho1 R_in² / r²
Outer surface
Q₂ = ρ₂ 4π R_out²
E₂ = 1 /ε₀ ρ₂ R_out² / r²
The total field is
E = E₁ + E₂
E = 1 /ε₀ | ρ | [- R_in² + R_out²] / r²
Let's calculate
E = 1 /8,854 10⁻¹² 250 10⁻⁹ [- 7² + 11²] / 12²
E = 1.412 10⁴ N / C
6) As the field is positive, it is directed radially with direction coming out of the sphere
Answer:
26.6°
Explanation:
refractive index of diamond, n = 2.23
When a ray of light passes from denser medium to the rarer medium and refracts at an angle of 90 degree from the normal of the surface, such angle of incidence in the denser medium is called the critical angle.
By the Snell's law
For critical angle, angle of incidence is critical angle, i = θc and angle of refraction, r = 90
So,
Sin θc / Sin 90 = 1 / 2.23
Sin θc = 0.448
θc = 26.6°
Thus, the critical angle is 26.6°.
Explanation:
The given data is as follows.
Electric field between plates without dielectric,
Electric field between the plates with dielectric, .
Permittivity of free space, =
Now, we will determine the charge density as follows.
=
=
Thus, we can conclude that the charge density on each surface of the dielectric is .