Electric Field Zero: Find Point Along Y-Axis

In summary, to find the electric field at the origin, you need to solve equations for "r" (distance), "E2-E1" (the electric fields at two points), and "k" (the charge at the origin). Once you have these three equations solved, you can use the quadratic formula to find the electric field at any point along the y-axis.
  • #1
itryphysics
114
0

Homework Statement



A charge of -3.02 micro C is located at the origin abd a charge of -2.44 micro C is located along the y-axis at 2.6109 m. At what point along the y-axis is the electric field zero?

Homework Equations


E = q/ r^2



The Attempt at a Solution



first i determined equations to use for "r" (distance)

r1 = y2 (2.6109m-y)^2
r2 =
I set the electric fields equal to zero

E2-E1 = o

k(2.44 micro C)/(6.8168-6.8168y=y^2) - k(3.02 micro C)/y2 =0

Then i just solved these as a quadratic in the end but the answer under the square root comes out as a negative or as a ridiculously large number. Please guide me through. Much appreciated!
 
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  • #2
k(2.44 micro C)/(6.8168-6.8168y=y^2) - k(3.02 micro C)/y2 =0

Wright this in the following form:
k(2.44 micro C)/(2.6109-y)^2 = k(3.02 micro C)/y^2
Take square root on both side and find the value of y. While writing down the answer you have mention from which charge you are measuring the distance y.
 
  • #3
why should i take the square root. I think the way i solved it and then used the quadratic formula in the end was much easier...
 
  • #4
(6.8168-6.8168y=y^2)
Check this one.
 
  • #5
oops sorry that was a typo . its (6.8168-6.8168y+y^2)
 
  • #6
[QUOTE=itryphysics;2041778]oops sorry that was a typo . its (6.8168-6.8168y+y^2)[/QUOTE]

It is also wrong.
(2,6109 - y)^2 = ?. Check it.
 
  • #7
argh! i had a brain spasm i guess...messed up on simple multiplication. Thank you so much for pointing that out!
now i got >> 6.8168-5.2218y+y^2
 
  • #8
so now I think I am going to set two equations equal to each other and then solve for y which will be my distance but I don't know which way i should set it up. Please suggest..

k(2.44 e-6 microC)/ (2.6109-d)^2 = k(3.02 e -6 micro C) / d2

Is it this way or do i need to swap around the denominators? please explain how you figure this out as well. Thanks
 
  • #9
Yes. Now you can proceed. Still taking square root is more easier.
 
  • #10
so my choice of denominators is correct?
 
  • #11
When you take square root on both side you get
(2.44 micro C)^1/2/(2.6109-y) = (3.02 micro C)^1/2/y
Now swap around the denominators and solve for y
 
  • #12
for my answer I am getting y= 1.37

I only have one last try left on my online homework program. Can you please check this with your answer to let me know if I committed any errors.Thanks!
 
  • #13
Your answer is correct.
 
  • #14
your help is greatly appreciated!
 

FAQ: Electric Field Zero: Find Point Along Y-Axis

What is an electric field?

An electric field is a force field that surrounds an electrically charged particle or object. It is a vector quantity that describes the direction and strength of the force that would be experienced by another charged particle placed in the field.

Why is finding the point where the electric field is zero important?

Finding the point where the electric field is zero is important because it allows us to determine the location of a neutral point, where the forces on charged particles cancel out and there is no net force. This can be useful in many applications, such as designing circuits or understanding the behavior of electric charges in a given space.

How do you find the point along the y-axis where the electric field is zero?

To find the point along the y-axis where the electric field is zero, you can use the equation E = kq/r^2, where E is the electric field, k is a constant, q is the charge, and r is the distance from the charge to the point along the y-axis. Set E equal to zero and solve for r to find the distance from the charge to the neutral point.

Can the electric field be zero at more than one point along the y-axis?

Yes, the electric field can be zero at more than one point along the y-axis. This will occur when there are multiple charges present, and the forces from each charge cancel out at different points along the y-axis.

How does the distance from the charge affect the location of the point where the electric field is zero along the y-axis?

The distance from the charge does affect the location of the point where the electric field is zero along the y-axis. As the distance increases, the electric field decreases and the neutral point will be further away from the charge. As the distance decreases, the electric field increases and the neutral point will be closer to the charge.

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