Given a square of sidelength a = 4 cm. We place a charged particle at each corner, three of them carry + 2 nC of charge and one carries the same amount of negative charge.
What is the magnitude of the electric field at the center of the square?
I read a previous post for a similar question, and tried to solve this question using the method that was given in response to that post.
I don't understand one thing, and I'm really confused about it.
When we're solving for the electric field at the center of the square, do we assume that there is a point charge located there? i.e. use Coulomb's law for the point charge and one of the charges at the corner? then mutiply the field found by that by 2.
Or would we find the electrostatic force acting on one charge, then use this charge to also find the electric field and mutilply this by 2?
Which is the correct way?
Sorry, my question got answered in a previous post.
Sorry for the repost!
I suppose you could put a sample 1 coulomb charge in the middle of the square.
To find the magnitude of the electric field at the center of the square, you would use the superposition principle. This principle states that the electric field at a point due to a collection of charges is the vector sum of the electric fields created by each individual charge.
In this case, you have four charges at the corners of the square, three of which are positive and one is negative. Let's consider the process step by step:
1. Calculate the electric field at the center due to each individual charge:
- Assume you have a point charge at one corner (charge A) and you want to find the electric field it creates at the center (point C). You can use Coulomb's law to calculate the electric field created by charge A at point C.
- Repeat this process for each of the four charges at the corners, considering each one as a point charge and finding the electric field it creates at the center.
2. Find the net electric field at the center:
- Since the electric field is a vector quantity, you need to take into account both the magnitude and direction of each individual electric field at the center. The electric fields created by the positive charges will point outward from the center, while the electric field created by the negative charge will point inward towards the center.
- To find the net electric field at the center, you add up (superpose) the individual electric fields by considering their magnitudes and directions. The positive electric fields will add up, and the negative electric field will subtract from the result.
So to summarize, you don't assume there is a point charge located at the center of the square. Instead, you calculate the electric field at the center due to each individual charge, and then find the net electric field at the center by considering the superposition of these individual electric fields.