Electric Field & Potential: Find Center of Square 2.0 cm

In summary, the electric field and potential at the center of a square with +9.0uC at one corner and -3.0uC at the remaining three corners can be calculated using the equation E= (K|qa|/r^2 + K|qc|/r^2) towards C, resulting in an electric field of 5.4x10^8 N/C towards C.
  • #1
NicoleKarmo
1
0

Homework Statement


Find the electric field and the potential at the center of a square 2.0 cm with charges of +9.0uC at one corner of the square and with charger of -3.0uC at the remaining 3 corners.


Homework Equations


the sum of Vi= the sum of KQi/ri


The Attempt at a Solution



I saw that the equation was re-arranged this way but I'm not sure how they arrived there:
E= Ea+Eb+Ec+Ed = Ea+Eb+Ec-Eb= Ea+Ec= (K|qa|/r^2 + K|qc|/r^2) towards C

when you plug in the #'s the answer is 5.4x10^8 N/C toward c.
what I don't understand is how they concluded that that was the formula to use.
 
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  • #2
Welcome to PF.

The E-field is a vector field.

The scalar form of the equation can be used to calculate the magnitude of the field at a point. But when you have multiple charges, then you have to pay attention to the direction of all the charges.

When calculating the field at the center then, the opposite corners of the square will act oppositely. Hence when you compare them, the corners with the same charges will offset (equal and like charges equidistant in opposite directions and all that).

That just means then that you need only calculate the magnitude of the different charges because ... well they will make different contributions.
 
  • #3


I would first clarify that the problem is referring to electric field and potential due to point charges, rather than a uniform electric field.

Next, I would explain that the formula used is based on the principle of superposition, which states that the total electric field and potential at a point due to multiple point charges is the sum of the individual fields and potentials at that point.

In this case, the electric field and potential at the center of the square can be found by adding the contributions from each individual charge. The formula used is a simplified version of the general formula for electric field, which takes into account the distance between the charges and the point of interest.

I would also mention that the direction of the electric field is toward the negative charge, as opposite charges attract each other.

Lastly, I would provide a step-by-step explanation of how to plug in the given values and arrive at the numerical answer.
 

Related to Electric Field & Potential: Find Center of Square 2.0 cm

1. What is an electric field?

The electric field is a physical quantity that describes the force exerted on a charged particle in an electric field. It is represented by a vector and is measured in units of newtons per coulomb (N/C).

2. How is the center of a square determined in terms of electric potential?

The center of a square can be determined by finding the point where the electric potential is equal on all sides. This means that the electric field lines are perpendicular to the sides of the square at this point.

3. How do I find the electric potential at a specific point in a square?

To find the electric potential at a specific point in a square, you will need to know the distance from that point to each of the four sides of the square, as well as the charge density on each side. Using these values, you can calculate the electric potential using the formula V = kQ/r, where k is the Coulomb constant, Q is the charge density, and r is the distance from the point to the side of the square.

4. What is the relationship between electric field and electric potential?

The electric field is the gradient of the electric potential. This means that the electric field is the rate of change of the electric potential with respect to distance. In other words, the electric field shows the direction and magnitude of the change in electric potential at a given point.

5. How does the center of a square affect the electric potential?

The center of a square is an important point in terms of electric potential because it is where the electric potential is equal on all sides. This means that the electric field lines are perpendicular to the sides of the square at this point, and the electric potential at this point is the same in all directions. This makes it a point of equilibrium in terms of electric potential.

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