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  • Can someone help me with this, The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 µC charge, its radius will

The energy stored in the electric field produced by a metal sphere is 4.5 J.  If the sphere contains 4 µC charge, its radius will
 

 

  • Option 1)

     20 mm

  • Option 2)

     32 mm

  • Option 3)

    28 mm

     

  • Option 4)

     16 mm

     

 

Answers (2)

As we learnt in 

Capacity of an Isolated Spherical Conductor -

C= 4\pi \epsilon _{0}R=\frac{1}{9\times 10^{9}}R

- wherein

 

 The energy stored in the electricity field produced by a metal sphere =4.5 J

4.5 = \frac{Q^{2}}{2C} \, \, \Rightarrow C = \frac{Q^{2}}{2\times 4.5}\, \, \, \, -(i)

Capicitance of spherical capacitor

C= 4\pi E_{_{0}}R=\frac{Q^{2}}{9}

R= \frac{1}{4\pi E_{0}}\times \frac{(4\times 10^{-6})^{2}}{9}= 9\times 10^{9}\times \frac{16}{9}\times 10^{12}

R= 16 \times 10^{-3}\, \, \, \, \, \Rightarrow R=16mm


Option 1)

 20 mm

Incorrect Option

Option 2)

 32 mm

Incorrect Option

Option 3)

28 mm

 

Incorrect Option

Option 4)

 16 mm

 

Correct Option

Posted by

Sabhrant Ambastha

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