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JenniferSmart1
Question: I solved the first part and I just need help understanding the second part. This will take me a a few min to write and draw....bear with me...
Point charges of \[q_1=-5.00 \mu C\]\[q_2=+3.00 \mu C\]\[q_3=+5.00\mu C\] located on the x access at \[x=-1.00cm\]\[x=0\]\[x=+1.00cm\]respectively. I calculated \[\vec{E}\] on the x axis atx=3.0cm and x=15.0cm and got: \[\vec{E}_{p1}=(1.14\times10^8N/C)\hat{i}\] and \[\vec{E}_{p1}=(1.74\times10^6N/C)\hat{i}\] Here is where I'm having trouble: ARe there any points on the x-axis where the magnitude of the electric field is zero? If so, where are those points?
@Luis_Rivera @phi
typo: I meant to write \[\vec{E}_{p2}=(1.74\times10^6N/C)\hat{i}\]
@Luis_Rivera I'll post the answer, can you help me understand it? I have the solution but I'm having a hard time understanding the concept
|dw:1360443203643:dw|
Think of it this way: if you were just slightly to the left of the particle at x = -1, the electric field would point to the right, correct?
Now go a hundred billion miles to the left. The distances between the three would be almost zero, so you'd really only be able to see a single particle of charge -5 + 3 + 5 = 3. Does that argument make sense?
Yes, so we would see a particle of charge three. Oh so is \[r\rightarrow \infty\]?
No. The point of that is if you're close to the one at -1, then the field points to the right. If you're far away, the field points to the left, so there must be some point at which the field is zero.
I guess that kinda makes sense....where from here?
The fields from the three particles are: \[E_1 = \frac{-5}{(x+1)^2} \] \[E_2 = \frac{3}{x^2} \] \[E_3 = \frac{5}{(x-1)^2} \] So the equation you should be solving is \[E_{total} = E_1 + E_2 + E_3 = 0 \]
\[E_1=\frac{q_1}{(x+1)^2}\] this means: the electric field due to a point charge from a positive test particle "x" located at a location (which I'm solving for) \[E_{total} = E_1 + E_2 + E_3 = 0\] by solving for x, I've found a place on the x axis where the electric field due to all point charges is zero....
makes sense. THanks @Jemurray3 !
The positive and negative charges are bothering me...|dw:1360445236763:dw|
What's bothering you?
I Would've written this as: \[-\frac{q_1}{(x-1)^2}-\frac{q_2}{x^2}-\frac{q_3}{(x+1)^2}=0\]
because the charge on q_1 is negative
You must also take into account the direction the field is pointing. The field from the q_1 charge is to the right.
Generally speaking \[ \vec{F} = \frac{kQ}{r^2} \hat{r} \] So Q is negative, but that is compensated by the direction of r hat.
That explains the positive sign, what about the x_1 part? why do they have it as x-(-1)?
I mean the x-1 part
That is the distance between a point (x) and the point (-1).
which should be x-1 though. That doesn't make sense in practice...I think.... Ok let's see (I can't believe I'm struggling with simple arithmetic) \[\triangle x=|x_2-x_1|\] so let's say our point is at x_2=-5 Oh I see....nevermind haha yep it's plus (+)
If you ever forget, just say "okay, so where is the distance zero?" and if it matches the location of the actual particle then you're good.
so (x+1) is zero at x=-1 , which is where the particle is.
yep, I'll remember that. Thanks again @Jemurray3 !!!