Question

A 18.5 µF spherical capacitor is composed of two metallic spheres, one having a radius twice as large as the other. If the region between the spheres is a vacuum, determine the volume of this region.

Answer 1

capacitance of spherical capacitor , air filled

                   C =4πε_o(ab / b-a )

Here a, b are radii of the spherical plates

Here given that b = 2a

therefore

                C =4πε_o ( 2a²/ a )

                   = 8πε_oa

So           a = C / 8πε_o

substitute given values

              a = 18.5 x 10^-6 F / 8 * 3.14 * 8.85 x 10 ^-12    

                = 8.32 x 10³ m

Therefore

           b =2a = 1.66 x 10 ⁴ m

............................................................................................................


Volume enclosed V enc = (4/3 ) πb³ - (4/3 ) πa³


                                                = (4/3 ) π { (2a) ³ - a³   }

      = (4/3 ) π(7a)³

Substitute 'a' value , we get

                                 = (4/3 ) π(7*8.32 x 10³)³

       V _enc = 1.68x 10¹³ m ³