Minimum distance for 1 pc charged particle fired at fixed 1 C charge

[neoclee]

Hi,
Can anyone possibly help me w/ this Question?
Been stuck trying to figure it out four a couple hours (what a waste...)
Thanks in advance!
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A charge of 1 C is fixed in place.
From a horizontal distance 10 km apart a particle of 1 g
and charge 1pc is fired with an initial speed 1000km/h towards the fixed charge.

What is the minimum distance between the two charges ?

I don't even know where to begin!
and what's pc ? Picocoloumbs ?

 

[MathStudent]

use conservation of energy...
do you know the equations for KE and PE?
yes pC is picocoulombs = 10^-12C

 

[neoclee]

i tried, but i can't get anything.
i don't know how PE is related to calculation of distance or radius,
can you atleast point to some formulas that show their relations ?

 

[MathStudent]

$$KE = \frac{1}{2} m v^2$$

$$PE = \frac{kq_1q_2}{r}$$

The second equation is the potential energy for two point charges where r is the distance between q1 and q2...

Remeber that conservation of energy means

$$KE_i \ + \ PE_i = KE_f \ + \ PE_f$$

Decide what should be the initial and final states, and set up the equation... the rest should be apparent from there

 

[neoclee]

Isn't that F=kq1q2/r^2 ?

Im trying it right now.
Thanks a lot for your help thus far.

 

[MathStudent]

Isn't that F=kq1q2/r^2 ?

Im trying it right now.
Thanks a lot for your help thus far.

Thats the equation for the electrical force between two point charges which isn't the same as electrical potential energy.

The potential energy equation is derived from that equation however.

 

[neoclee]

Iv tried to use the help youve provided me to find the answer.
can you please take a look at the attachment and see if my understanding is right and if iv approached the problem properly ?
[The known/unknown values are listed on my first post.]

Thanks again, you help means a lot.

 

[MathStudent]

Where's the attachment?

 

[neoclee]

Sorry, i thought i added them [file limited was exeeded; had to edit them]...

 

[MathStudent]

before even checking if your calculations are correct... you need to go over units

v needs to be in m/s , and g needs to be in kg

 

[neoclee]

they are...I didn't include the unites, but everything is in m/s and KG
edit: actually i missed a deci place for KG, ill have to fix it now..

 

[MathStudent]

oh yeah,, you had the velocity right, I just didn't recognize it

 

[MathStudent]

also in calc1.gif, the equation for KE is 0.5mv^2, you forgot to square the velocity.

 

[neoclee]

Iv made the revision.
Can you please take a look now ?
Thanks again..

 

[MathStudent]

The first part is ok...

in the second, why did you multiply KE_i by PE_i, where in the equation does it say to multiply them?

 

[neoclee]

Changed...
Will you take a look one last time ? {thanks}

 

[MathStudent]

Success!

 

[neoclee]

lol,
so i take it as that's the right answer...
(its a shame i made so many unnecesary mistakes, Univeristy works really getting up to me...but phys not my area :) ) My friends were saying , i could only solve this problem w/ integration. i guess not ;)

Thanks a lot for all your help. I really really appreciate your time towards this.

 

[MathStudent]

no problem... glad I could help