A nervous physicist worries that the two metal shelves of his wood frame bookcas

Question

A nervous physicist worries that the two metal shelves of his wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance (in F) of the empty shelves if they have area 2.80 times 10^-1 m^2 and are 0.280 m apart? _____ F (b) What is the voltage between them (in V) if opposite charges of magnitude 2.10 nC are placed on them? ____ V (c) To show that this voltage poses a small hazard, calculate the energy stored (in J). _____ J

Explanation / Answer

Given that

charge q=2.1nC

area A=2.8*10^-1 m^2

distance d=0.28 m

basing on the concept of parallel plate capacitor

now we find the capacitance

capacitance C=8.85*10^-12*2.8*10^-1/0.28=88.5*10^-13 F

now we find the potential difference

potential difference V=Q/C=2.1*10^-9/88.5*10^-13=237.3 v

now we find the energy stored

the energy stored E=1/2cv^2=1/2*88.5*10^-13*237.3^2=2491774.6*10^-13=2.5*10^-5 J

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