How to Calculate the Electric Field at Point M?

In summary, Gauss' Law states that the electric field due to a charge is a function of the charge and its distance from another charge. To find the electric field at a point, you need to know the charges and their distances from each other. Gauss' Law can be used to find the electric field at a point, but it can also be used to calculate the forces between charges.
  • #1
caz1429
3
0
I've been a reader of this forum last year, but now I've registered and need help understanding electric field.

1. Homework Statement
Four charges q1 = q3 = -q and q2 = q4 = +q, where q = 7 µC, are fixed at the corners of a square with sides a = 1 m.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys212/fall08/homework/01/01/cl10.gif
So 4 charges are on the corners of a square. Top-left and lower-right are -q, and Top-right and lower-left are +q. I need to calculate the x-component of the electric field at the bottom of the square in the middle at point M. The sides of the square are 1m.2. Homework Equations
Gauss' Law3. The Attempt at a Solution
I attempted to draw where the electric field points and it is to the left. When I attempt the problem though everything cancels out and leaves me with zero.

The two bottom charges should cancel out (?) leaving two charges at the top. Pyth. thereom finds the radius to the top two corners sq(1.25)=d

Ex= cos(45)(K)(+Q)/d^2+cos(45)(K)(-q)/d^2 = 0
What am I doing wrong? This is an old homework question with no chance of getting points, but I'm trying to understand it to prepare for an upcoming test. I'm also kind of confused about Gauss' Law. Do you pretend an electron is at the bottom of the square, calculate the force, then divide by q? The answer also asks for N/C while other problems ask for N. Can anyone give me any general units of the electric field? Any help would be appreciated.
1. Homework Statement
 
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  • #2
caz1429 said:
The two bottom charges should cancel out ...

Not so. Think carefully about the direction of the E field due to:
1. The negative charge that is to the right of the point, and
2. The positive charge that is to the left of the point.
 
  • #3
The electric field due to the left charge would point right and the field from the right charge would also point right? How would you go about calculating that? When I try to get an answer I always get zero still.
 
  • #4
caz1429 said:
The electric field due to the left charge would point right and the field from the right charge would also point right? How would you go about calculating that? When I try to get an answer I always get zero still.

Since they both point to the right, just add up the two numbers. The direction will still be to the right.
Since they are both positive numbers, you will not get zero when you add them up.

(Then there's still the two charges at the top to consider...)
 
  • #5
Thanks a lot for pointing me in the right direction Redbelly98, things finally clicked. Now let's go celebrate a Cubs win!
 
  • #6
You're welcome! And welcome to PF.
 

FAQ: How to Calculate the Electric Field at Point M?

What is the equation for the electric field at a point due to four charges on a square?

The equation for the electric field at a point due to four charges on a square is given by E = k * (Q/R^2), where k is the Coulomb's constant, Q is the charge of the point charge, and R is the distance between the point charge and the center of the square.

How do the individual charges influence the electric field at a point in the square?

The individual charges on the square will create their own electric fields that combine to form the overall electric field at a point. The direction and strength of each individual field will depend on the charge and distance from the point.

Can the electric field at a point be zero when there are four charges on a square?

Yes, the electric field at a point can be zero when there are four charges on a square. This can occur when the charges are arranged in such a way that their electric fields cancel each other out, resulting in a net electric field of zero at that point.

How does the direction of the electric field change as the distance from the square increases?

As the distance from the square increases, the direction of the electric field will change. At closer distances, the electric field will be stronger and will point towards or away from the individual charges depending on their signs. As the distance increases, the field will become weaker and may eventually become zero.

Are there any other factors that can affect the electric field at a point due to four charges on a square?

Yes, other factors such as the size and shape of the square, as well as the presence of other charges in the vicinity, can also affect the electric field at a point due to four charges on a square. These factors may alter the overall strength and direction of the electric field at a given point.

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