Help with Point Charges and Charge by Contact

[talebone]

1. Homework Statement

Three small identical metal spheres carry electric charges, +Q, +2Q, and +3Q. The centres of the spheres lie in a straight line at fixed positions R, S and T, such that the distance between the spheres at R and S is d1 and that between the spheres at S and T is d2. Assume that the distances between the spheres is large in comparison with their size, and that the charges on the spheres act like point charges.

Q1
The sphere at S will experience a zero net electric force when d2 is equal to
A 3d1
B d1/3
C √3 d1
D d1/√3

Q2
A small metal sphere (identical to those at R, S, T) carrying a charge of-2Q is first brought into contact with the sphere at R, and then into contact with the sphere at S, and finally into contact with the sphere at T. After making contact with the three spheres, in the stated order, the charge on the sphere at T is
A +3Q
B +15Q/4
C +15Q/8
D +4Q

2. Homework Equations

F=kQ1Q2/r²
3. The Attempt at a Solution

Q1 - SOLVED thanks
k(Q)(2Q)/d1² = k(2Q)(3Q)/d2²
k2Q/d1² = k6Q/d2²
d2² = k3Q(d1²)/k3Q
d2 = √3Q d1

Q2
1. at R, the net charge will be -Q. so each sphere will have -0.5Q
2. at S, the net charge will be +1.5Q. so each sphere will have +0.75Q
3. at T, the net charge will be +3.75Q, so each sphere will have +1.875Q

which ANS C gives so I guess that's the answer. but I'm not sure why the equation is worded like that. thanks for your time :) appreciate it

 

[hms.tech]

k(Q)(2Q)/d1² = k(2Q)(3Q)/d2²

k3Q/d1² = k5Q/d2²
d2² = k5Q(d1²)/k3Q
d2 = √2Q d1

I see an arithmetic error !

And as far as the 2nd question is concerned, you will have work out the amount of charge gained/lost keeping in mind that the total charge is conserved

 

[talebone]

where is the error? maybe I'm tired but I've looked over it a hundred times!

ok second questions let's try:

1. at R, the net charge will be -Q. so each sphere will have -0.5Q
2. at S, the net charge will be +1.5Q. so each sphere will have +0.75Q
3. at T, the net charge will be +3.75Q, so each sphere will have +1.875Q

which ANS C gives so I guess that's the answer. but I'm not sure why the equation is worded like that. thanks for your time :) appreciate it

 

[DimReg]

For the arithmetic error, you're making a mistake in the second line (right after you set up the problem). I think you're adding instead of multiplying. Try cancelling first.

Also, it looks like you subtracted instead of dividing in the last step.

 

[talebone]

yeah dumb me. thanks!

k(Q)(2Q)/d12 = k(2Q)(3Q)/d22
k2Q/d12 = k6Q/d22
d22 = k3Q(d12)/k3Q
d2 = √3Q d1

 

[DimReg]

I don't know if it's a typo or not, but you forgot to cancel another factor of Q so your answer should be (without the Q):

d2 = √3 d1

Note that no Q appears in the final answer, and it shouldn't. Cause then you're answer would be in units of length = length*charge, which is just inconsistent.

 

[talebone]

thanks for pointing that out, typed it by accident. any clue on the second question?

 

[hms.tech]

Your answer is correct for the 2nd part as well :)

 

[talebone]

hms, thanks for that but the way I got my ANS does not give me the format shown in the list of answers. could you give me a clue as to how the given ANS is formatted as such? thanks.

 

[haruspex]

hms, thanks for that but the way I got my ANS does not give me the format shown in the list of answers. could you give me a clue as to how the given ANS is formatted as such? thanks.

You got 1.875. The answer formats are whole numbers and fractions. So try expressing your answer as a fraction.

 

[talebone]

ok. say I ignored the +/- on each charge. if I added all the charges available (2, 1, 2, 3) that's 8 charges. is that where the 8 comes from? but I can't imagine where 15Q comes from.

 

[haruspex]

I don't understand your puzzlement - perhaps I never did.
You obtained the answer 1.875Q. You recognise this is the same as an offered answer, 15Q/8. What still bothers you?

 

[talebone]

Lol haruspex I can see your point. I'm just wondering why they chose to express it as a fraction instead of 1.875Q. I guess I thought maybe there was an easier way to arrive at the answer than the way I did. There probably isn't, thanks for your patience.