A Van de Graaff generator has a spherical dome of radius 12 cm. Operating in dry air, where "atmospheric breakdown" is at E_max= 3.0 *10⁶ N/C, what is the maximum charge that can be held on the dome? (k_e = 8.99 *10⁹ N.m²/C²)

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The maximum charge that can be held on the dome is given by:Q = 4πε0r2Emaxwhere:ε0 is the permittivity of free space (8.85 x 10^-12 C^2/Nm^2)r is the radius of the dome (0.12 m)Emax is the maximum electric field strength (3.0 x 10^6 N/C)Plugging in these values, we get:Q = 4π(8.85 x 10^-12 C^2/Nm^2)(0.12 m)^2(3.0 x 10^6 N/C)Q = 4.8 x 10^-6 CTherefore, the maximum charge that can be held on the dome is 4.8 x 10^-6 C.

A Van De Graaff Generator Has a Spherical Dome of Radius