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JEE Main 2023 (10 Apr, Shift 1) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from JEE Main 2023 (10 Apr, Shift 1)

Q68JEE Main 2023 · 10 APR · SHIFT 1Difficult

Electric Potential & Equipotentials

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities σ,−σ\sigma, -\sigma and σ\sigma respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is _________ cm.

Numerical answer type. Work it out, then open the answer.

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Answer: 5

  1. VX=σε0(a−b+c)V_X = \frac{\sigma}{\varepsilon_0}(a - b + c), VZ=σε0⋅a2−b2+c2cV_Z = \frac{\sigma}{\varepsilon_0}\cdot\frac{a^2 - b^2 + c^2}{c}
  2. VX=VZ⇒c(a−b)+c2=a2−b2+c2⇒c=a+bV_X = V_Z \Rightarrow c(a - b) + c^2 = a^2 - b^2 + c^2 \Rightarrow c = a + b
  3. c=2+3=5 cmc = 2 + 3 = 5\,\text{cm}
  4. So the radius of Z is 5 cm.
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