Practice quiz, don\'t really know where to start. Please help, show a lot of ste

Question

Practice quiz, don't really know where to start. Please help, show a lot of steps please! Thanks!

Two pith balls of Radius R, mass M and charge Q are suspended from a point hih above as shown.

The length of the String is L

1.  

a. Start from NII and show that the charge on each ball can be written as

b. Show that the unites of the rhs of the equation are what you expect

c. Show that the formula makes sense in at least one limiting case.

Two pith balls of Radius R, mass M and charge Q are suspended from a point hih above as shown. The length of the String is L Start from NII and show that the charge on each ball can be written as Q = 4 Mg(L + R)2 sin2(A/2)tan (A/2)/kE Show that the unites of the rhs of the equation are what you expect Show that the formula makes sense in at least one limiting case.

Explanation / Answer

so each ball makes an angle of A/2 from the vertical and length to middle of ball is L + R

so sum forces in the y

T cos(A/2) - m g = 0
T = m g/cos(A/2)

sum forces in the x
F electric - T sin(A/2) = 0

k Q^2/r^2 - T sin(A/2) = 0
plug in for T
k Q^2/r^2 = m g tan(A/2)

but r/2 = (L + R) sin(A/2)
so r = 2 (L+R) sin(A/2)

so Q^2 = 4 mg (L+R)^2 sin^2(A/s) tan(A/2)/k

so Q = sqrt( 4 mg (L+R)^2 sin^2(A/s) tan(A/2)/k)

b)
rhs units are
remember units of k are given by N = [k] C^2/m^2
so unit of k are N m^2/C^2
sqrt( N m^2/(Nm^2/C^2) = sqrt(C^2) = C

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