A Van de Graaff generator has a spherical dome of radius 50.0 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) A)1.7E-4 C B)8.3E-5 C. C)4.2E-6 C D)8.3E-5 C E)1.7E-6 C

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Quizplus · Accepted Answer

The maximum charge can be calculated using the formula for the electric field at the surface of a sphere: $E = \frac{k \cdot Q}{r^2}$, where $E$ is the electric field, $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$), $Q$ is the charge, and $r$ is the radius of the sphere. Rearranging the formula to solve for $Q$ gives $Q = \frac{E \cdot r^2}{k}$. Substituting the given values ($E = 3.0 \times 10^6 \, \text{N/C}$, $r = 0.5 \, \text{m}$, and $k = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$) into the formula yields $Q = \frac{3.0 \times 10^6 \cdot (0.5)^2}{8.99 \times 10^9} = 8.3 \times 10^{-5} \, \text{C}$.

A Van De Graaff Generator Has a Spherical Dome of Radius