# Magnitude and DIRECTION of electric field of a square.

• johnknee
In summary, the magnitude of the electric field at the center of a square with sides of 42.5cm, where one corner has a charge of -38.2μC and the other three corners have charges of -26.9μC each, is 1.11*10^-6 N/C. The direction of the electric field can be determined by considering the direction a positive charge would move if placed in the field.

## Homework Statement

Calculate the magnitude of the electric field at the center of a square 42.5cm on a side if one corner is occupied by a −38.2μC charge and the other three are occupied by −26.9μC charges. (This part done)

Choose the correct direction of the electric field at the center of the square.
A.outward of −38.2μC charge
B.perpendicular to the diagonal passing through −38.2μC charge
C.toward to −38.2μC charge

Not sure how to approach the directions part.

## Homework Equations

E = kQ/r^2
Magnitude E = ((Ex)^2 + (Ey)^2)^1/2

## The Attempt at a Solution

r = 0.425m
E1 = kQ1/r^2 = ((9*10^9)(38.2*10^-6))/0.3^2 = 3.8*10^6 N/C
E2 = E3 = E4 = ((9*10^9)(26.9*10^-6))/0.3^2 = 2.7*10^6 N/C

I then solved each of their x and y components, and added them together. Net Ex is -787000 and net Ey is 787000.

Resultant = ((-787000)^2 + (787000)^2)^1/2 = 1.11*10^-6 N/C

I am not sure how I would figure out the direction part.
*I am thinking towards the - 38.2 charge

Last edited:
johnknee said:
I am thinking towards the - 38.2 charge
The direction of the field is the direction a positive charge would tend to move if placed in the field. Does that fit with your answer? (I'm not hinting either way.)

## 1. What is the magnitude of the electric field at the center of a square?

The magnitude of the electric field at the center of a square is determined by the formula E = kQ/a², where k is the Coulomb's constant, Q is the charge of each side of the square, and a is the length of one side of the square.

## 2. How does the direction of the electric field change as you move away from the center of a square?

The direction of the electric field at any point around a square is always radial, pointing away from the center of the square. As you move away from the center, the direction of the electric field will remain radial but may change in orientation as the angle between the field lines and the sides of the square changes.

## 3. Is the direction of the electric field the same on all sides of a square?

No, the direction of the electric field can vary on each side of a square. On opposite sides of the square, the field will point in opposite directions, while on adjacent sides, the field will point in the same direction.

## 4. How does the magnitude of the electric field change as you move away from the square?

As you move away from the square, the magnitude of the electric field decreases. This is because the electric field follows an inverse square law, meaning that it decreases with the square of the distance from the source.

## 5. Can the direction of the electric field be negative?

No, the direction of the electric field is always positive and points away from a positive charge and towards a negative charge. However, the magnitude of the electric field can be negative if the charge is negative.