A) A general rule for estimating the capacitance C of an isolated conducting sph

Question

A) A general rule for estimating the capacitance C of an isolated conducting sphere with radius r is C(in pF) r(in cm). That is, the numerical value of C in pF is about the same as the numerical value of the sphere’s radius in cm. Justify this rule.

B) Modeling the human body as a 1 m radius conducting sphere, use the given rule to estimate the average capacitance for an adult.

C) While walking across a carpet, you acquire an excess “static electricity” charge Q and produce a 0.5 cm spark when reaching out to touch a metallic door knob. The dielectric strength of air is 30 kV/cm. Use this information to estimate Q (in C)

Explanation / Answer

Capacitance of the sperical Condcutor is C = 4pi eo R

so

C is in direct proportion with R

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C = 4*3.14* 8.85 e -12 * 1

C = 111.11 pF

--------------------------------------------------------------

Electric field E = KQ/r^2

here E = 3000/1e-2 = 3 e6 V/m

so

Charge Q = Er^2/K

Q = (3e6 * 0.005 * 0.005)/(9e9)

Q = 8.34 nC

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