Answered: What total (excess) charge q must the…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter13: Chemical Reactions

Section: Chapter Questions

Problem 1FIB

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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 3.0 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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$E l e c t r i c f i e l d, E = 3 \times 10^{6} N / C R a d i u s, r = 3 \times 10^{- 2} m C o u l o m b' s c o n s \tan t, k = \frac{1}{4 {πε}_{o}} = 8.99 \times 10^{9} N m^{2} / C^{2} w h e r e ε_{o} is the permitivity S u r f a c e a r e a o f a n a t o m, A_{a t o m} = 0.015 \times 10^{- 18} m^{2}$

The equation for electric field due to charged surface density is

$E = 2 πσk (1 - \frac{z}{\sqrt{z^{2} + r^{2}}}) where σ is the surface charge density$

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