Net Electric Field at the center of a square

In summary, the net electric field at the center of the square, with edge lengths of 24.00cm and charges of q1=8.0e-6C, q2=-8.0e-6C, q3=-8.0e-6, and q4=+8.0, can be found by breaking it into components using the magnitude and direction of the total field. The E-field from q1 and q3 will cancel out, while the E-field from q2 and q4 will contribute to the total field. The vector diagram can be used to determine the x and y components of the total field.
  • #1
kemcco1955
3
0

Homework Statement


What net electric field do the particles of problem #1 produce at the square's center? Problem number one has a square with edge lengths of 24.00cm and charges of q1==8.0e-6C, q2=-8.0e-6C, q3=-8.0e-6, and q4=+8.0. He wants the answer for the electric field in component form(Etotal= N/C x + N/Cy. I do not know how to find electric field when using different components.


Homework Equations


Ecenter=kq/r^2


The Attempt at a Solution


I know that q1 and q3 cancel/ equal zero because they are both negative and on the diagonal from one another. The vector for q2 points away from the charge and the vector for q4 points toward the charge. I find E2 using (8.99e9)(-8e-6)/.1697^2. And for E4 I get the same but with an opposite sign. The r it got to be .1697 m by taking the sqrt of .24^2+.24^2 =.3394/2=.1697. The angel, I think is 45 degrees. I am having difficulty finding how to get the E total into components I know that you can take an answer and multiply it by cos45 and sin45(which are the same), but I don't know how to set up the vectors to solve...I hope that makes some since...I am very confused.
 
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  • #2
Hi kemcco1955,

kemcco1955 said:

Homework Statement


What net electric field do the particles of problem #1 produce at the square's center? Problem number one has a square with edge lengths of 24.00cm and charges of q1==8.0e-6C, q2=-8.0e-6C, q3=-8.0e-6, and q4=+8.0. He wants the answer for the electric field in component form(Etotal= N/C x + N/Cy. I do not know how to find electric field when using different components.


Homework Equations


Ecenter=kq/r^2


The Attempt at a Solution


I know that q1 and q3 cancel/ equal zero because they are both negative and on the diagonal from one another. The vector for q2 points away from the charge and the vector for q4 points toward the charge.

No, q2 is a negative charge, so its field points toward itself. q4 is a positive charge so its field points away from itself.

I find E2 using (8.99e9)(-8e-6)/.1697^2. And for E4 I get the same but with an opposite sign. The r it got to be .1697 m by taking the sqrt of .24^2+.24^2 =.3394/2=.1697. The angel, I think is 45 degrees. I am having difficulty finding how to get the E total into components I know that you can take an answer and multiply it by cos45 and sin45(which are the same), but I don't know how to set up the vectors to solve...I hope that makes some since...I am very confused.

Draw the E total vector with the magnitude labelled and with the correct direction. Then it's just a matter of breaking it into x and y components like any other vector. For example,

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec5

Of course, depending on which direction the E-field is pointing, you might get one or both components to be negative.
 

FAQ: Net Electric Field at the center of a square

What is a net electric field?

A net electric field refers to the combined effect of all electric fields present in a given region or point in space. It is a vector quantity that represents the direction and strength of the overall electric field at a specific location.

How is the net electric field at the center of a square calculated?

The net electric field at the center of a square can be calculated by finding the vector sum of the individual electric fields at the center. This can be done by using the principle of superposition, which states that the net effect of multiple electric fields is the sum of their individual effects.

What factors affect the net electric field at the center of a square?

The net electric field at the center of a square is affected by the magnitude and direction of the individual electric fields present, as well as the distance from the center of the square to each point charge creating the electric fields.

How does the net electric field at the center of a square differ from the corners?

The net electric field at the center of a square is generally stronger than at the corners because the distance from the center to each point charge is shorter. Additionally, the direction of the net electric field at the center may differ from that at the corners, depending on the arrangement of the point charges.

What are some real-world applications of the concept of net electric field at the center of a square?

The concept of net electric field at the center of a square is important in understanding and analyzing electric fields in various situations, such as in electronic devices, electric circuits, and even in the human body. It is also used in engineering and design processes for creating and optimizing systems that rely on electric fields.

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