(1) A long cylindrical shell carries a uniform charge density. If there is +0.10
ID: 1706286 • Letter: #
Question
(1) A long cylindrical shell carries a uniform charge density. If there is +0.100 C per meter, what is the volume charge density of this cylinder with an inner radius of 5 cm, and outer radius of 10 cm?(2) For problem 1, illustrate (qualitatively) the electrical field and the equi-potential surfaces generated by this charge distribution.
(3) Eight identical spherical rain drops are each at a potential V, relative to the potential far away. They coalesce to make one spherical rain drop. What is the electrical potential of the resulting large rain drop?
Explanation / Answer
volume of a part of length L. V=S*L=L*pi*(0.1^2-0.05^2)=0.024L. so charge density D=0.1*L/V=0.1*L/(0.024L)=0.1/0.024=4.24(C/m3). ---------- electric field lines: go straight from the center of the cylinder. (radius's directions) equi-potential is many cylinder with the radius that larger than 10cm. -------------------- let the charge and radius of one rain drop be Q and R. V~Q/R. when 8 drops coalesce 8R^3=R'^3. 8Q=Q'. so R'=2R. so V'~Q'/R'=8Q/2R=4V V'=4V.
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