Question

a spherical condenser has 10cm and 12cm as the radii of inner and outer spheres. the space between the two spheres is filled with a dielectric of dielectric constant 5. the capacity when (1) the outer sphere is earthed​

Answer 1

Explanation:

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Answer 2

The capacity when the outer sphere is earthed​ is 3.34 × 10^-10 F.

Given: Radii of inner sphere = 10 cm,  Dielectric constant (k) = 5

           Radii of outer sphere = 12 cm.

To Find: The capacity when the outer sphere is earthed​

Solution:

• The capacitance of a capacitor is defined as the ratio of the magnitude of charge on either of the conductor plates to the potential difference existing between the conductors. The SI unit of capacitance is coulomb per volt or farad (F).
• The dielectric constant of a material determines the amount of energy that a capacitor can store when voltage is applied.
• Capacitance of the spherical conductor when the outer surface is grounded is given by the formula,

                   C = 4πε0.k.( r1 × r2 / ( r2 - r1 ))

where, k = dielectric constant, r1 = inner radius, r2 = outer radius

and k = 5, r1 = 10 cm, r2 = 12 cm

∴ C = 4πε0.k.( r1 × r2 / ( r2 - r1 ))

      = 4 × 22/7 × 8.85 × 10^-12 × 5 × [ 0.1 × 0.12 / ( 0.12 - 0.10 )]

      = 3.34 × 10^-10 F

Hence, the capacity when the outer sphere is earthed​= 3.34 × 10^-10 F.

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