Three concentric spherical shells have radii a, b and c (a A, VB and VC denote the potentials of the three shells, then, for c = a+b, we havea)VC = VB ≠ VAb)VC ≠ VB ≠ VAc)VC = VB = VAd)VA = VC VBCorrect answer is option 'D'. Can you explain this answer?

Question

Three concentric spherical shells have radii a, b and c (a A, VB and VC denote the potentials of the three shells, then, for c = a+b, we havea)VC = VB ≠ VAb)VC ≠ VB ≠ VAc)VC = VB = VAd)VA = VC > VBCorrect answer is option 'D'. Can you explain this answer?

Answer

Explanation:
To analyze the potential of each spherical shell, we can consider Gauss's law. According to Gauss's law, the electric field inside a conductor is zero. Therefore, the potential inside each spherical shell is constant.

Case 1: VC = VB ≠ VA
If VC = VB, it means that the potentials of the outer and middle shells are equal. However, VA is not equal to VC and VB. This implies that the potential of the innermost shell is different from the other two shells. Therefore, this case is not valid.

Case 2: VC ≠ VB ≠ VA
If VC ≠ VB ≠ VA, it means that all three potentials are different. This implies that the potential of each shell is unique and not equal to the others. Therefore, this case is not valid.

Case 3: VC = VB = VA
If VC = VB = VA, it means that the potentials of all three shells are equal. This implies that the potential is constant throughout the entire region enclosed by the spherical shells. Therefore, this case is not valid.

Case 4: VA = VC > VB
If VA = VC > VB, it means that the potentials of the innermost and outermost shells are equal, while the potential of the middle shell is different. This implies that the potential decreases as we move from the outer shell to the middle shell, and remains constant from the middle shell to the innermost shell. Therefore, this case is valid.

Hence, the correct answer is option 'D' - VA = VC > VB.

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