1. A solid sphere of radius R=10cm has a uniform charge Q=2.0E-8 C. The sphere r
ID: 1767940 • Letter: 1
Question
1. A solid sphere of radius R=10cm has a uniform charge Q=2.0E-8 C. The sphere
rotates on one of its diameters with uniform angular velocity w=10 rad/s. What is
the current density at r=5 cm ? (note angular velocity w = 2pi/T, where T is the
period of rotation)
answer should be in A/m^2
2. As Figure 1 shows, Daniel Cell is made up of two concentric cylinders. The outer
cylinder is made from copper with length l=20cm and radius b=12cm. The inner
cylinder is made from zinc with radius a=4cm.The resistivity of the liquid between
them is p=0.6 Omega/cm. What is the internal resistance of the cell?
answer should be in omega
Explanation / Answer
Using cylindrical coordinates around the axis of the cylinder, consider a thin cylinder element of depth dr at distance r The resistance of that element for the full cylinder length is dR = ?*dr/A, where A = 2*?*r*L (the nominal surface area of the cylindrical element).
dR = integration( p*dr/(2*pi*r*L) )
Integrate
dR = p/(2*pi*L) integrate ( (1/r)*dr)
R = p/(2*pi*L) * ln(r) [r = a to b)
R = p/(2*pi*L) * [ln(b) - ln(a)]
R = p/(2*pi*L) * ln(b/a)
= 0.6/(2*pi*20) * ln(12/4)
= 5.2455 X 10^-3 ohm
current density is a function of both r and theta.
current density is given by, j = rho * w * r * sin(theta)
here rho = Q/ (4*pi*r^3/3) = 4.77 * 10^-6
w = 10 rad/s
r = 5cm = 0.05m
therefore j = 2.387*10^-6 sin(theta) A/m^2
morover, this link contains the whole derivation and information. it will surely clear all your doubts :)
http://www.slideshare.net/FFMdeMul/b-field-homogenous-sphere
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