Consider two concentric conducting spherical shells as shown in the figure.
The inner shell has a radius a and carries a charge +Q. The outer shell has
a radius b and carries a charge -Q. The empty space between them is half-
filled by a hemispherical shell of a dielectric having permittivity &1. The
remaining space between the shells is filled with air having the permittivity
Eo.
(A)
E0
a
1,;.
- Q
E1
+Q
Dielectric
The electric field at a radial distancer from the center and between the shells
(a <r<b) is
2 T (E0+E1) 12
everywhere
on the air side
and
(B)
(C)
(D)
Q
on the air side
2 T E0 72
4T (EotE) pa everywhere
and
4Tt tEn pe on the dielectric side
2 rey pe on the dielectric side
Options:
(A) E0 a 1,;. - Q E1 +Q Dielectric The electric field at a radial distancer from the center and between the shells (a <r<b) is 2 T (E0+E1) 12 everywhere on the air side and
(B)
(C)
(D) Q on the air side 2 T E0 72 4T (EotE) pa everywhere and 4Tt tEn pe on the dielectric side 2 rey pe on the dielectric side
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.41 / PH Q.31)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Special theory of relativity* (`Lorentz Transformations & Relativistic Invariants`) | **Section**: *Section 2: Classical Mechanics*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **Special theory of relativity**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **A**.
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