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NEET PHYSICSELECTROSTATIC POTENTIAL AND CAPACITANCEMedium

Question

Two hollow conducting spheres of radii R1R_1 and R2R_2 (R1≫R2R_1 \gg R_2) are concentric and have equal charges. The potential would be:

A

dependent on the material property of the sphere

B

more on the bigger sphere

C

more on the smaller sphere

D

equal on both the spheres

Step-by-Step Solution

  1. Setup: Consider two concentric conducting spherical shells. Let the radius of the outer sphere be R1R_1 and the inner sphere be R2R_2 (given R1≫R2R_1 \gg R_2). Both have equal positive charge QQ.
  2. Potential of Inner Sphere (Small): The potential at the surface of the inner sphere (VsmallV_{small}) is the sum of the potential due to its own charge and the potential due to the outer sphere surrounding it. Inside a charged shell, potential is constant and equal to the surface value. Vsmall=Vself+Vdue_to_outer=kQR2+kQR1V_{small} = V_{self} + V_{due\_to\_outer} = \frac{kQ}{R_2} + \frac{kQ}{R_1}.
  3. Potential of Outer Sphere (Big): The potential at the surface of the outer sphere (VbigV_{big}) is the sum of the potential due to its own charge and the potential due to the inner sphere (which acts as a point charge at the center for points outside). Vbig=Vself+Vdue_to_inner=kQR1+kQR1=2kQR1V_{big} = V_{self} + V_{due\_to\_inner} = \frac{kQ}{R_1} + \frac{kQ}{R_1} = \frac{2kQ}{R_1}.
  4. Comparison: Comparing terms: The term kQR1\frac{kQ}{R_1} is common to both. The difference lies in the first term: kQR2\frac{kQ}{R_2} vs kQR1\frac{kQ}{R_1}. Since R2<R1R_2 < R_1, it follows that 1R2>1R1\frac{1}{R_2} > \frac{1}{R_1}. Therefore, Vsmall>VbigV_{small} > V_{big}.
  5. Conclusion: The potential is higher on the smaller sphere. (This concept is analogous to gravitational potential discussed in Class 11 Physics, Chapter 8, where potential inside a shell is constant).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ELECTROSTATIC POTENTIAL AND CAPACITANCE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSELECTROSTATIC POTENTIAL AND CAPACITANCEhollowconductingspheresconcentriccharges

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