Problem 3: Angle between suspended charges Two charges of identical mass m, one

Question

Problem 3: Angle between suspended charges Two charges of identical mass m, one with charge q, the other with charge 2q, hang from strings of length 1 from a common point. Assume q is sufficiently weak so that any angle you're looking for is very small, and find an approximate expression for the angle each charge makes with respect to the vertical. Check (show us!) that the units work out, and that the limiting behaviour for large mass, large length, and/or small q are at least sensible. Problem 4: Delta functions and charge distributions In problem 1, we had two point charges: +3q located at x--D, and -q located at x+D. Write an expression for the volume charge density (r) of this system of charges. Now consider a thin spherical shell of radius R (Fig 2.11 in Griffiths) which carries a (b) uniform surface of this c integrate are correct.) charge density . Write an expression for the volume charge density (r) harge distribution. (Hint: use spherical coordinates, and be sure that your total d charge comes out right. Verify explicitly that the units of your final expression

Explanation / Answer

Problem 3)

electric force F = kq x 2q/r2, (where r = 2 Lsin)

gravity = mg

tan = F/(mg) = kq2/(2mgL2sin2)

for small angle, tan sin

So, Angle, = [kq2/(2mgL2)]1/3

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