Explanation:
Gauss Law relates the distribution of electric charge to the resulting electric field.
Applying Gauss's Law,
EA = Q / ε₀
Where:
E is the magnitude of the electric field,
A is the cross-sectional area of the conducting sphere,
Q is the positive charge
ε₀ is the permittivity
We be considering cases for the specified regions.
Case 1: When r < R
The electric field is zero, since the enclosed charge is equal to zero
E(r) = 0
Case 2: When R < r < 2R
The enclosed charge equals to Q, then the electric field equals;
E(4πr²) = Q / ε₀
E = Q / 4πε₀r²
E = KQ /r²
Constant K = 1 / 4πε₀ = 9.0 × 10⁹ Nm²/C²
Case 3: When r > 2R
The enclosed charge equals to Q, then the electric field equals;
E(4πr²) = 2Q / ε₀
E = 2Q / 4πε₀r²
E = 2KQ /r²
