Electric Force and Charged Spheres

In summary, electric force is a fundamental force that results from the interaction between charged particles. It can be attractive or repulsive and is calculated using Coulomb's law. A charged sphere is an object with a net electric charge distributed evenly on its surface, and its electric field is directly proportional to its charge and inversely proportional to the distance from its center. The electric field inside a charged sphere is zero due to the Faraday cage effect.
  • #1
Soaring Crane
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0

Homework Statement



Consider the following configuration of fixed, uniformly charged spheres on an xy coordinate system:
·a blue sphere fixed at the origin with positive charge q.
·a red sphere fixed at the point (d1,0) with unknown charge q_red,
·a yellow sphere fixed at the point (d2*cos theta, -d2*sin theta) with unknown charge q_yellow.

The net electric force on the blue sphere is observed to be vector F = (0,-F), where F>0 .

Here is a makeshift sketch:

O = charged particle

O_(q)___________O (d1, 0) q_red
--\
---\
----\O (d2*cos theta, -d2*sin theta) q_yellow

in which the dotted line between q at (0,0) and q_yellow is d2 and theta = angle between d2 and the x-axis (The x- axis is depicted by __________ pattern.)

What is the sign of the charge on the yellow sphere?
What is the sign of the charge on the red sphere?



Homework Equations



Possibly Coulomb’s Law:

F_mag = (k*|q1*q2|)/(r^2), where k = 8.988 * 10^9 N*m^2/C^2



The Attempt at a Solution



The y-component of the electric force is –F. The q_red particle does not have a y-component; it only has an x-component. The q_yellow charge has a y-component. If a – sign follows, then the q_yellow chage is positive since – indicates repulsion?


Is the q_red charge negative? If the electric force’s x-component is 0, then q_red’s x-component must be negative if q_yellow’s x-component is positive?

Thanks.
 
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  • #2


I would like to clarify a few points and provide a solution to the problem presented.

Firstly, it is important to note that Coulomb's Law is indeed applicable in this scenario, as it describes the relationship between the electric force and the distance between charged particles. However, it is not necessary to use this equation to solve the problem.

Now, to answer the questions posed:

1. What is the sign of the charge on the yellow sphere?

Based on the given information, we know that the net electric force on the blue sphere is pointing downwards (negative y-direction). This means that there must be a repulsive force between the blue and yellow spheres. Since like charges repel, we can conclude that the yellow sphere must have the same positive charge as the blue sphere. Therefore, the sign of the charge on the yellow sphere is positive.

2. What is the sign of the charge on the red sphere?

Similarly, since the net electric force on the blue sphere is pointing downwards, there must be an attractive force between the blue and red spheres. This means that the red sphere must have the opposite charge as the blue sphere. Therefore, the sign of the charge on the red sphere is negative.

In summary, the yellow sphere has a positive charge and the red sphere has a negative charge. I hope this explanation helps.
 
  • #3


I would first clarify the assumptions and equations being used in this scenario. The sketch and problem statement suggest that Coulomb's Law is being used to calculate the electric force between the spheres, but it should be noted that this equation only applies to point charges, not spheres. Additionally, the assumption of fixed and uniformly charged spheres may not accurately represent real-world situations.

With that being said, the sign of the charge on the yellow sphere cannot be determined solely from the given information. The fact that the y-component of the electric force on the blue sphere is negative does not necessarily mean that the charge on the yellow sphere is positive. It is possible that the yellow sphere has a negative charge and is being attracted to the positive charge on the blue sphere. More information, such as the distance between the spheres and the magnitudes of the charges, would be needed to determine the signs of the charges on the spheres.

The same applies to the red sphere. The fact that it only has an x-component of electric force does not necessarily mean that its charge is negative. It could also be neutral or have a small positive charge that is being balanced by the force from the blue sphere.

In summary, the sign of the charge on the yellow and red spheres cannot be determined from the given information. More data and a more accurate model would be needed to make a conclusive determination.
 

What is electric force?

Electric force is a fundamental force of nature that results from the interaction between charged particles. It can be either attractive or repulsive, depending on the charges of the particles involved.

How is electric force calculated?

The electric force between two charged particles is calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

What is a charged sphere?

A charged sphere is an object that has a net electric charge and is in the shape of a sphere. The charge can be either positive or negative, and it is evenly distributed throughout the surface of the sphere.

What is the electric field of a charged sphere?

The electric field of a charged sphere is the force per unit charge experienced by a test charge placed at a point in the space surrounding the sphere. It is directly proportional to the charge of the sphere and inversely proportional to the square of the distance from the center of the sphere.

How is the electric field inside a charged sphere?

The electric field inside a charged sphere is zero, as the electric force from all the charges on the surface of the sphere cancel out at every point inside the sphere. This is known as the Faraday cage effect.

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