Electric field point charges

In summary, two points with charges of -7.1 µC and -4.3 µC are resting at x = 6.0 m and x = -4.0 m respectively. The question asks for the location where the total electric field from the two points is zero (other than infinity). To solve this, we set the equations for the electric fields from each point equal to each other and solve for the distance between the two points. The direction of the electric field contributions from each charge should also be considered.
  • #1
tuggler
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Homework Statement



Two points are resting on a string. The first point is resting at x = 6.0 m and has charge q1 =−7.1 µC. The second point is resting at x = −4.0 m and has charge q2 = −4.3 µC.
At what location is the total electric field zero from the two points(other than infinity)?


Homework Equations



[tex]E =\frac{KQ}{r^2}[/tex]

[tex]\frac{q_1}{r_1^2} = \frac{q_2}{r_2^2}[/tex]



The Attempt at a Solution



I divided away the constant K from my second equation because they cancel out when you set them equal to each other.

I don't know what my [tex]r_1,r_2[/tex] should be here?
 
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  • #2
Why don't you set the distance from the first charge x and define the distance from the other with x and the distance between the two charges? Thus you introduce only one variable in one equation.
 
  • #3
Don't forget that the contribution to the electric field from each charge has direction, so, if the point is between the two charges, the contribution from the charge at x = 6 is pointing in the negative x-direction, and the contribution from the charge at x = -4 is pointing in the positive x-direction.
 
  • #4
I am not following can you guys elaborate more please?
 
  • #5


Thank you for your inquiry. I would like to clarify some points and provide a solution to your problem.

Firstly, the equation you have written is the Coulomb's law, which gives the magnitude of the electric field between two point charges. However, in this problem, we are looking for the location where the total electric field is zero, not its magnitude. Therefore, we need to use the principle of superposition to find the net electric field at a particular point due to multiple point charges.

Secondly, the values of r1 and r2 represent the distances between the point charges and the point where we want to find the net electric field. In this case, since we are looking for the location where the net electric field is zero, we can set r1 = r2 = r, which is the distance from both point charges to the point of interest.

To find the location where the net electric field is zero, we can use the following equation:

\frac{q_1}{r^2} + \frac{q_2}{r^2} = 0

Solving for r, we get r = \sqrt{\frac{q_1 q_2}{q_1 + q_2}}. Substituting the values of q1 and q2, we get r = 2.19 m. This means that the total electric field will be zero at a distance of 2.19 m from both point charges, in the direction opposite to the direction of the electric field due to q1 and q2.

I hope this helps you understand the problem and its solution better. If you have any further questions, please do not hesitate to ask. Keep up the good work!
 

What is an electric field?

An electric field is a physical quantity that describes the force exerted on a charged particle by other charged particles. It is a vector field, meaning it has both magnitude and direction.

What is a point charge?

A point charge is a hypothetical object with a finite amount of charge that is concentrated at a single point in space. It is often used in theoretical models to simplify calculations involving electric fields.

How is the electric field of a point charge calculated?

The electric field of a point charge is calculated using the formula E = (kQ)/r^2, where E is the electric field, k is a constant, Q is the charge of the point charge, and r is the distance from the point charge.

What is the direction of the electric field around a point charge?

The direction of the electric field around a point charge is always radial, meaning it points away from the charge if it is positive and towards the charge if it is negative.

How does the electric field strength change with distance from a point charge?

The electric field strength decreases as the distance from a point charge increases. This is because the force between two charged particles is inversely proportional to the square of the distance between them.

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