A hollow insulated conducting sphere is given a positive charge of 10μC. What will be the electric field at the center of the sphere if its radius is 2 meters?
(a) Zero
(b) 5μC/m²
(c) 20μC/m²
(d) 8μC/m²

Question Analysis:
The problem involves finding the electric field at the center of a hollow conducting sphere that is given a positive charge of 10 μC10 \, \mu C, with a radius of 2 meters.
Key Concept: Electric Field Inside a Conductor
1. Gauss's Law:
According to Gauss's Law, the electric field inside a conducting sphere is zero at all points within the conducting material. For a hollow conductor, this also applies to the cavity inside the sphere.
Mathematically:
∮E⃗⋅dA⃗=qenclosedϵ0\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\epsilon_0}
o qenclosed=0q_{\text{enclosed}} = 0 for any Gaussian surface inside the hollow region of the sphere. Hence, the electric field inside is: E⃗=0\vec{E} = 0
2. Charge Distribution in a Hollow Conductor:
In a hollow conducting sphere:
o The entire charge resides on the outer surface of the sphere.
o Inside the cavity, the net electric field is zero because the charge on the outer surface does not contribute to the field inside (as per the shell theorem).
3. Conclusion: The electric field at the center of a hollow conducting sphere is always zero, regardless of the amount of charge or the radius of the sphere.
Solution:
Given:
• Charge on the sphere, q=10 μCq = 10 \, \mu C
• Radius of the sphere, R=2 mR = 2 \, \text{m}
The electric field at the center of the sphere is:
E=0 N/CE = 0 \, \text{N/C}
Correct Answer:
(a) Zero\boxed{(a) \, \text{Zero}}