A +10 micro coloumb charge is situated at the center of a small sphere of surface area 400 cm². FInd the electric field leaving the sphere.
To find the electric field leaving the sphere, we can use Gauss's law. Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.
In this case, the sphere is closed and has a charge of +10 micro Coulomb at its center. Since the sphere is symmetric, we can apply Gauss's law to calculate the electric field.
Step 1: Find the electric flux through the surface of the sphere.
The electric flux (Φ) is given by Φ = E * A, where E is the electric field and A is the surface area of the sphere.
Given that the surface area of the sphere is 400 cm², we need to convert it to square meters:
A = 400 cm² = 400 * (10^-4) m² = 0.04 m²
Step 2: Calculate the charge enclosed by the sphere.
Since the charge of +10 micro Coulomb is at the center of the sphere, the entire charge is enclosed by the sphere.
Step 3: Apply Gauss's law to find the electric field.
Since Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed, we have:
Φ = Q / ε₀, where Q is the charge enclosed by the surface and ε₀ is the vacuum permittivity constant (8.854 x 10^-12 C²/N m²).
Substituting the values, we have:
E * A = Q / ε₀
E * 0.04 m² = 10 μC / (8.854 × 10⁻¹² C²/N m²)
Step 4: Solve for the electric field (E).
E = (10 μC / (8.854 × 10⁻¹² C²/N m²)) / 0.04 m²
Calculating the value gives:
E ≈ 2.83 x 10⁹ N/C
Therefore, the electric field leaving the sphere is approximately 2.83 x 10⁹ N/C.