Verified Solution • 2025–26 Session moderate

QJEEM17Phbc7e: JEE Main 2017 Physics - Class 12 JEEM17Phbc7e Solution: The energy stored in the electric field produced by a metal…

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 μ\mu C charge, its radius will be :
[ Take : 14 π∈0={1 \over {4\,\pi { \in _0}}} = 9 ×\times 109 N −- m2/C2 ]

Multiple Choice Options

  • A 20 mm
  • B 32 mm
  • C 28 mm
  • D 16 mm

Step-by-Step Verified Solution

Energy of sphere = Q22C{{{Q^2}} \over {2C}}

∴   \therefore\,\,\, 16×10−122C{{16 \times {{10}^{ - 12}}} \over {2C}} = 4.5

⇒\Rightarrow    \,\,\, C = 16×10−129{{16 \times {{10}^{ - 12}}} \over 9}

We know capacity of spherical conductor,

C = 4 π\pi ε\varepsilon 0R

∴   \therefore\,\,\, 4 π\pi ε\varepsilon 0R = 16×10−129{{16 \times {{10}^{ - 12}}} \over 9}

⇒\Rightarrow    \,\,\, R = 14πε0×16×10−129{1 \over {4\pi {\varepsilon _0}}} \times {{16 \times {{10}^{ - 12}}} \over 9}

= 9 ×\times 109 ×\times 16×10−129{{16 \times {{10}^{ - 12}}} \over 9}

= 16 mm

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