How far apart would parallel pennies have to be to make a 1.00-pF capacitor? Doe

Question

How far apart would parallel pennies have to be to make a 1.00-pF capacitor? Does your answer suggest that you are justified in treating these pennies as infinite sheets? Explain. What is the capacitance of a capacitor that consists of two concentric spherical metal shells? The inner radius of the outer shell is a, and the outer radius of the inner shell is b. Check your result by considering the limiting case in which the gap between the conductors is much smaller than b. In that limit, the formula for the capacitance of the flat, parallel plate capacitor ought to be applicable. What do the equipotential surfaces look like for a pair of point charges +q and -q separated by a finite distance? Draw a sketch, and try to convince yourself that your sketch makes sense by determining a mathematical expression for the surfaces. Consider two parallel infinite line charges both having linear charge density A with one along the z-axis, and another passing through the point (l, 0). What do the equipotential surfaces look like? Find a mathematical expression for the equipotential curves in the x-y plane, and show that it can be written in the form p(x, y) = C where p(x, y) is a quadratic polynomial in x and y and C is a constant.

Explanation / Answer

1.

radius of penny

r=1 cm

area of penny

A=piR2=pi*0.012=3.14*10-4 m2

Capacitance

C=eoA/d

therefore seperation between pennies is

D=eoA/C

D=(8.8542*10-12)(3.14*10-4)/(1*10-12)

D=2.78*10-3 m =2.8 mm

Yes it is a good approximation

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