Electrostatics net force question

[TheRedDevil18]

Homework Statement

I am having a problem with 8.4. I get an answer but it does not match the answer in the memo which I think is wrong.

Homework Equations

The Attempt at a Solution

8.1) T to P (Could someone explain why?)

8.2) Q = (3*10^-9)-(6*10^-9)/2
= -1.5*10^-9 (This is the charge on each sphere, right?)

Charge gained by P = (-1.5*10^-9)-(3*10^-9) = -4.5*10^-9

8.3) -4.5*10^-9/-1.6*10^-19 = 2.81*10^10 electrons

8.4) P on R

I will just get to the answer
1.62*10^-7 N right (Repulsive)

T on R

4.05*10^-8 N left (Repulsive)

So the net force on R would be:
1.62*10^-7+4.05*10^-8 = 2.03*10^-7 N right

The answer in the memo subtracted the two forces. Who is right?

 

[gneill]

Homework Statement

I am having a problem with 8.4. I get an answer but it does not match the answer in the memo which I think is wrong.

Homework Equations

The Attempt at a Solution

8.1) T to P (Could someone explain why?)

8.2) Q = (3*10^-9)-(6*10^-9)/2
= -1.5*10^-9 (This is the charge on each sphere, right?)

Charge gained by P = (-1.5*10^-9)-(3*10^-9) = -4.5*10^-9

Or you could say that sphere P LOST 4.5 x 10^-9 Coulombs, right?

8.3) -4.5*10^-9/-1.6*10^-19 = 2.81*10^10 electrons

8.4) P on R

I will just get to the answer
1.62*10^-7 N right (Repulsive)

T on R

4.05*10^-8 N left (Repulsive)

So the net force on R would be:
1.62*10^-7+4.05*10^-8 = 2.03*10^-7 N right

The answer in the memo subtracted the two forces. Who is right?

You're doing okay up to 8.4, as you surmised. Something's gone wrong in 8.4. Can you give details on your workings? Pay special attention to the directions that the forces will act on sphere R.

 

[TheRedDevil18]

Or you could say that sphere P LOST 4.5 x 10^-9 Coulombs, right?

You're doing okay up to 8.4, as you surmised. Something's gone wrong in 8.4. Can you give details on your workings? Pay special attention to the directions that the forces will act on sphere R.

I think the problem you are referring to is the net force?, if so then the answer should be, 1.62*10^-7 + (-4.05*10^-8) = 1.22*10^-7 N right.
Could you explain 8.1 for me?, and could you explain why sphere P lost 4.5*10^-9 coulombs, I mean it was positive so didnt it gain electrons to become negative?

 

[gneill]

I think the problem you are referring to is the net force?, if so then the answer should be, 1.62*10^-7 + (-4.05*10^-8) = 1.22*10^-7 N right.

That looks better.

Could you explain 8.1 for me?, and could you explain why sphere P lost 4.5*10^-9 coulombs, I mean it was positive so didnt it gain electrons to become negative?

For the metal spheres, electrons are the mobile charge carriers; The positive charges are fixed in place as the nuclei of the atoms. So it is electrons that move when charges move. However, by convention we say (or assume) that currents are moving positive charges. This works out fine because by symmetry, a movement of some given amount of negative charge (carried by electrons in this case) from point A to point B is mathematically identical to an identical amount of positive charge being moved from B to A. It is always conventional current that refer to unless otherwise specified.

Sphere P started with +3 x 10^-9 Coulombs on it, and ended up at -1.5 x 10^-9 Coulombs. So in terms of conventional charge and current, it lost 4.5 x 10^-9 Coulombs.

 

[TheRedDevil18]

Sphere P started with +3 x 10^-9 Coulombs on it, and ended up at -1.5 x 10^-9 Coulombs. So in terms of conventional charge and current, it lost 4.5 x 10^-9 Coulombs.

So it gained electrons from sphere T to become negative?, and sphere T lost electrons to become less negative?

 

[gneill]

So it gained electrons from sphere T to become negative?, and sphere T lost electrons to become less negative?

Yes, that is the underlying mechanism of what occurred. As I stated, electrons are the actual mobile charge carriers even though we "pretend" that it's positive charges that are moving.