A square conducting slab with 7 m sides carries a net charge of 89 mu or micro CC.
what is the electric field?
To find the electric field produced by the charged square conducting slab, we can use the formula for electric field produced by a uniformly charged flat sheet:
E = σ / (2 * ε₀)
where E is the electric field, σ is the charge density (charge per unit area) and ε₀ is the vacuum permittivity constant (≈ 8.854 × 10^(-12) C²/N·m²).
First, let's find the charge density, σ.
The charge on the square slab is Q = 89 µC = 89 × 10^(-6) C, and the area of the slab is A = 7 * 7 = 49 m².
So, the charge density is:
σ = Q / A = (89 × 10^(-6) C) / (49 m²) ≈ 1.8163 × 10^(-6) C/m²
Now, we can find the electric field using the formula:
E = σ / (2 * ε₀) ≈ (1.8163 × 10^(-6) C/m²) / (2 * 8.854 × 10^(-12) C²/N·m²) ≈ 102,528 N/C
Thus, the electric field produced by the charged square conducting slab is approximately 102,528 N/C.
To find the electric field due to a charged conducting slab, you can use the following formula:
Electric field (E) = charge density (σ) / (2 * ε₀)
Where:
- Electric field (E) is the strength of the electric field
- Charge density (σ) is the total charge divided by the area of the conducting slab
- ε₀ is the permittivity of free space, which is a constant equal to 8.85 x 10^(-12) C²/(N·m²)
Given:
Side length of the square slab (a) = 7 m
Net charge of the slab (Q) = 89 μC (microCoulombs)
Area of the square slab (A) = a²
Charge density (σ) = Q / A
Plugging in the values:
Area of the square slab (A) = (7 m)² = 49 m²
Charge density (σ) = (89 μC) / (49 m²)
Now, we need to convert the charge from microCoulombs to Coulombs:
1 μC = 10^(-6) C
Therefore, 89 μC = 89 x 10^(-6) C
Calculating:
Charge density (σ) = (89 x 10^(-6) C) / (49 m²)
Finally, plugging in all the values into the formula for the electric field:
Electric field (E) = charge density (σ) / (2 * ε₀)
Electric field (E) = [(89 x 10^(-6) C) / (49 m²)] / (2 * 8.85 x 10^(-12) C²/(N·m²))
Calculating this equation will give you the electric field.
To find the electric field due to a charged conducting slab, we can use the formula:
Electric field (E) = Charge density (σ) / (2 * ε₀),
where σ is the surface charge density and ε₀ is the permittivity of free space.
In this case, the net charge of the conducting slab is given as 89 μC (microcoulombs). However, we also need to know the surface area of the slab to calculate the charge density (σ).
The surface area of a square slab is given by the formula: A = s² (where s is the side length), so the surface area of the slab in this case is 7 m * 7 m = 49 m².
To calculate the charge density (σ), we divide the net charge (89 μC) by the surface area (49 m²):
σ = 89 μC / 49 m²
Now, we substitute the value of σ into the formula for electric field:
E = σ / (2 * ε₀)
We need to know the value of ε₀, which is the permittivity of free space. The value of ε₀ is approximately 8.854 × 10⁻¹² F/m (Farads per meter).
Substituting the values:
E = (89 μC / 49 m²) / (2 * 8.854 × 10⁻¹² F/m)
Evaluating this expression will give us the magnitude of the electric field in units of volts per meter (V/m).