A spherical conductor of 20cm radius of charged to the maximum it can be before

Question

A spherical conductor of 20cm radius of charged to the maximum it can be before the is dielectric breakdown in the surrounding air.

Supplemental data is included in case you need it.

Speed of light in vacuum c = 2.998 Times 108 m/s Planck's constant h = 6.626 Times 10-34 J.s Acceleration due to Earth's gravity g = 9.81 m.s-2 Dielectric breakdown strength of air EB = 3 Times 106N.C-1 Dielectric permittivity of space epsilon0 = 8.85 Times 10-12 F.m-1 Coulomb's constant k = 8.99 Times 109 N.m2.C-2 Fundamental charge e = 1.602 x 10-19 C

Explanation / Answer

E = k Q/R^2

==> Q = E R^2/k = 3e6*0.20*0.20/8.99e9 = 1.33 x 10^-5 C

==> V = k Q/R = 8.99e9*1.335e-5/0.20 = 6.00 x 10^5 V

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