# The ring has radius r and it is spinning at angular

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e) A very thin plastic ring has a constant linear charge density, and total charge Q. The ring has radius R and it is spinning at angular velocity ω about its center (which is at the origin). What is the current I, in terms of given quantities? Also, how would you write down the volume current density Jin cylindrical coordinates? (This may be a little tricky, since the ring is "very thin", there will be some delta functions involved. I suggest trying to write down a formula forρ(r,φ,z) first. And, remember that Jshould be a vector!)Q6. B FIELD FROM ROTATING DISK In the previous problem, you had a CD (radius R) with a fixed, constant, uniform surface electric charge density σeverywhere on its top surface. It was spinning at angular velocity ωˆ z about its center (the origin). You hopefully found the current density Kat a distance r from the center. Use that result to find the magnetic field B(0,0,z) at any distance z directly above the origin. Does your answer seem reasonable? Please check it, with units, and some limiting behaviors (e.g. what do you expect if R0? z→∞? ω→0? Slightly less "obvious", but also worth checking/thinking about, what about z0? B(0,0,z)0 for some of these limits: can you tell me howthey go to zero as a function of z?) Hint: you might find Griffith’s Example 5.6 interesting. B? z R