Answer:
Explanation:
a) To find the surface charge density at the point on the conductor surface, we can use the equation: E = σ/ε. Where E is the electric field at the point, σ is the surface charge density, and ε is the permittivity of free space.
Given E = 15ax - 8az V/m, we can see that there is no electric field component in the y-direction. Therefore, the surface charge density must also be zero in the y-direction.
We can find the surface charge density in the x-direction by equating the x-components of the electric field and the surface charge density:
15a = σ/ε
Solving for σ, we get:
σ = 15aε
Substituting the value of ε (ε = ε0), we get:
σ = 15aε0
Therefore, the surface charge density at the point on the conductor surface is 15aε0 C/m2.
b) The electric displacement field D just outside the conductor is related to the surface charge density σ by the equation:
D = εE
where E is the electric field just outside the conductor.
Since the conductor is an equipotential surface, the electric field just outside the conductor is perpendicular to the surface and has a magnitude given by:
E = σ/ε0
Substituting this in the above equation, we get:
D = ε0 (σ/ε0)
D = σ
Substituting the value of σ (-20 nC/m2), we get:
D = -20 nC/m2
Therefore, the electric displacement field just outside the conductor is -20 nC/m2.
To answer your question, we need to consider the following terms:
1. Electric field E
2. Surface charge density σ
3. Permittivity of free space ε0
Given that E = 15ax - 8az V/m at a point on the conductor surface, we can find the surface charge density σ using the formula:
σ = ε0 * E_n
where E_n is the normal component of the electric field on the surface (which is -8az V/m in this case) and ε0 is the permittivity of free space (8.854 x 10^-12 F/m).
σ = (8.854 x 10^-12 F/m) * (-8 V/m)
σ = -71.032 x 10^-12 C/m²
Thus, the surface charge density at that point is -71.032 pC/m².
For part b), since the region y ≥ 2 is occupied by a conductor with surface charge -20 nC/m², we can find the electric displacement D just outside the conductor. D is related to the surface charge density σ using the equation:
D = σ
In this case, σ = -20 nC/m² = -20 x 10^-9 C/m².
So, D = -20 x 10^-9 C/m² just outside the conductor.