How much charge is enclosed by the box?

In summary, the conversation discusses the use of Gauss's Law to determine the charge enclosed by a box with a side length of 2.54 cm positioned at the origin of a rectangular coordinate system. The uniform electric field, given by E= 4 N/C(i) + 5 N/C(j) + 6 N/C(k), cancels out in all directions due to the equal area of the box's sides. Therefore, the final conclusion is that there is no enclosed charge.
  • #1
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1. A box with a side of length L=2.54 cm is positioned with one of its corners at the origin of a rectangular coordinate system. There is a uniform electric field
E= 4 N/C(i) + 5 N/C(j) + 6 N/C(k).
How much charge is enclosed by the box?


2. I believe I should be using Gauss's Law (Epsilon=permittivity of free space)
Ie= Q/Epsilon
Ie= ExA
Area=L^2



3. I basically multiplied all sides with its proper vector x area. The area for all sides seems to be the same since all L=2.54cm=.0254m.
Area came out to be 6.4516X10^-4 m^2.
I came out with a charge=Q=0
Not quite sure if I am calculating this correctly; please help.
 
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  • #2
Since you have not shown all your steps, it's impossible to say whether you are doing it correctly. Since the field is uniform, there is certainly no enclosed charge.
 
  • #3
Yes. That is correct to say that there is no charge since the electric field is uniform.
Area was the same all around so the electric flux canceled each other out in the i, j, z directions. Q=0.
Thanks for your help.
 

1. What does it mean to have charge enclosed by a box?

The term "charge" refers to the property of particles that causes them to interact with each other through the electromagnetic force. When we say "charge is enclosed by a box," we are referring to the amount of charge contained within a closed boundary or volume.

2. How is the amount of enclosed charge calculated?

The amount of enclosed charge can be calculated by adding up the charges of all the particles within the box. This can be done by measuring the individual charges of each particle and adding them together, or by using equations that relate charge to other physical quantities such as electric field or potential.

3. Does the shape or size of the box affect the amount of enclosed charge?

Yes, the shape and size of the box can affect the amount of enclosed charge. This is because the number of particles and their distribution within the box can vary depending on its shape and size. Additionally, the electric field and potential within the box can also be affected by its shape and size, which in turn can affect the amount of enclosed charge.

4. Can the amount of enclosed charge vary over time?

Yes, the amount of enclosed charge can vary over time. This is because particles can move in and out of the box, which can change the total amount of charge within it. Additionally, external factors such as electric fields or currents can also influence the amount of enclosed charge over time.

5. Why is it important to know how much charge is enclosed by a box?

Knowing the amount of charge enclosed by a box is important for understanding the behavior of electric and magnetic fields within the box. It can also help in predicting and analyzing the interactions between charged particles within the box. In practical applications, knowing the enclosed charge can also be useful in designing and controlling electrical and electronic systems.

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