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(a) What total (excess) charge q must the disk in the figure have for the electric field on the surface of the disk at its center to have the magnitude 3.0 × 106 N/C, the E value at which air breaks down electrically, producing sparks? Take the disk radius as 4.9 cm. (b) Suppose each surface atom has an effective cross-sectional area of 0.015 nm2. How many atoms are needed to make up the disk surface? (c) The charge calculated in (a) results from some of the surface atoms having one excess electron. What fraction of these atoms must be so charged?

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Final answer:

To find the total charge of the disk, use the formula q = E * r² / k. The number of atoms making up the disk surface can be found by dividing the total surface area by the effective cross-sectional area of each atom. To find the fraction of atoms with an excess electron, divide the excess charge by the charge of a single electron and then divide by the total number of atoms.

Step-by-step explanation:

To determine the total charge of the disk, we can first calculate the electric field at the surface using the formula E = k*q / r², where k is the electrostatic constant, q is the charge, and r is the radius of the disk. Rearranging the formula, we find that q = E * r² / k. Plugging in the values given, we get q = (3.0 * 10^6 N/C) * (0.049 m)² / (9.0 * 10^9 Nm²/C²). Solving this equation gives us the value of q.



To calculate the number of atoms making up the disk surface, we can divide the total surface area of the disk by the effective cross-sectional area of each atom. The surface area of the disk can be calculated using the formula A = π * r². Dividing this area by the effective cross-sectional area of each atom gives us the number of atoms.



To determine the fraction of atoms that must be charged, we can divide the excess charge on the disk by the charge of a single electron (1.602 * 10^-19 C). This will give us the number of excess electrons. Dividing this number by the total number of atoms on the disk surface will give us the fraction.

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