What is the Point of Zero Electric Field?

In summary, The point (other than infinity) at which the electric field is zero is outside the two charges, with a distance of 0.57 meters from the center of the two charges. The forces on a hypothetical charge q from q1 and q2 are equal and opposite, and the direction of the force is determined by the sign of the charge.
  • #1
Keithkent09
33
0

Homework Statement


In the figure below (q1 = -2.3 µC, q2 = 6.80 µC), determine the point (other than infinity) at which the electric field is zero. (Figure is attached)

Homework Equations


E=k*Q/r^2
F-k*q_1*q_2/r^2
F-Q*E

The Attempt at a Solution


I thought about finding where the force is zero and then the electric field would be zero because of F=Q*E. But I did not think that that was correct.
 

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  • #2
Hi Keith! :smile:

(try using the X2 tag just above the Reply box :wink:)
Keithkent09 said:
I thought about finding where the force is zero and then the electric field would be zero because of F=Q*E. But I did not think that that was correct.

No, that's fine … F = qE, so they're zero together. :smile:

(btw, i think it's usually little q for charge, except big Q for the charge of a black hole :wink:)
 
  • #3
Alright I get that part.
So then I set the two forces equal to each other and k*q_1*q_2/x^2=k*q_2*q_1/(d-x)^2
Is that the correct set up?
 
  • #4
Keithkent09 said:
So then I set the two forces equal to each other and k*q_1*q_2/x^2=k*q_2*q_1/(d-x)^2
Is that the correct set up?

erm :redface: … what about q (or Q) ? :wink:
 
  • #5
Um you mean the F=qE part?
If that is the case then the q is just the overall charge right and I am given two qs so I am not sure what that translates as...
 
  • #6
Keithkent09 said:
…the q is just the overall charge right and I am given two qs so I am not sure what that translates as...

No, q isn't "the overall charge", it's a hypothetical "test" charge.

Your …
Keithkent09 said:
k*q_1*q_2/x^2=k*q_2*q_1/(d-x)^2

… cancels out to give 1/x2 = 1/(d-x)2.

You need the forces on a hypothetical charge q to be equal and opposite.
 
  • #7
Yeah I did that earlier and I got x to be .5 using d=1 meter.
However this answer is not correct. Was my algebra just bad or is there something more to the problem. Sorry I am just having a tough time.
 
  • #8
Keithkent09 said:
Yeah I did that earlier and I got x to be .5 using d=1 meter.
However this answer is not correct. Was my algebra just bad or is there something more to the problem. Sorry I am just having a tough time.

That's because your k*q_1*q_2/x^2=k*q_2*q_1/(d-x)^2 is wrong.

You need the force on q from q1 to be equal to the force on q from q2
 
  • #9
So that leaves me with q_1/x^2=q_2/(d-x)^2?
 
  • #10
Yes. :smile:
 
  • #11
Alright good. I got x=.57. This does not seem to be the right answer and I think this leaves me to be in between the two charges instead of to the left of them. What is the next step or did I do something incorrectly again?
 
  • #12
ah, they have opposite charge, so the equilibrium position will be outside, so you need to use d+x instead of d-x. :smile:
 
  • #13
Do I include the negative signs for the charges or is it the absolute value of those charges I cannot remember?
 
  • #14
Good morning Keith! :smile:

(just got up :zzz: …)

To find the direction of a force, you must include the sign of the charge. :wink:
 

Related to What is the Point of Zero Electric Field?

1. How do you calculate the electric field at a point?

The electric field at a point is calculated by taking the product of the magnitude of the charge and the distance from the point to the charge, divided by the square of the distance. This can be represented by the equation E = kQ/r^2, where k is the Coulomb's constant, Q is the charge, and r is the distance.

2. What is the significance of finding zero electric field?

Finding zero electric field at a point means that there is no net electric force acting on any charged particles at that point. This can be useful in determining the equilibrium position of a charged particle or in analyzing the behavior of an electric field.

3. What factors can affect the electric field at a point?

The electric field at a point can be affected by the magnitude and distribution of charges in the surrounding area, as well as the distance and orientation of these charges from the point in question. Additionally, the presence of conductive or insulating materials can also impact the electric field.

4. How does electric field relate to potential energy?

The electric field is directly related to the potential energy of a charged particle. The electric potential at a point is equal to the electric potential energy per unit charge at that point. This means that a stronger electric field will result in a higher potential energy for a charged particle in that field.

5. Can the electric field at a point ever be negative?

Yes, the electric field at a point can be negative. This simply means that the direction of the field is opposite to the direction of the force that would be exerted on a positive test charge at that point. A negative electric field does not necessarily mean that there is a negative charge present, as the direction of the field can be affected by the distribution of charges around the point.

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