# Electric Field and Electric Potential

• katie_lynn16
In summary, to find the magnitude of the electric field at the center of the square, you can use the equation E = deltaV/r and calculate the electric field at each corner, then sum the values to get the total electric field at the center.
katie_lynn16
Hey there, I am new to this site and was wondering if anyone could help me with a problem I'm stuck on:

The electric potential is given at the four corners of a 1 cm square: V1 = 1.6 V, V2 = 12.4 V, V3 = 1.6 V, V4 = -9.2 V. What is the magnitude of the electric field at the centre of the square?

This seems like it should be easy, but for some reason I just can't get it.

Attempt:

Ok, I know that E=deltaV/r and V=kq/r and E= kq/r^2
I've tried finding the differences in the voltage, V1-v2, v2-v3, v3-v4 and v4-v1. then i could find the electric field at that point. Since the voltages arent the same, then the electric field at the center isn't zero.

I'm just really stuck and think that I'm making it harder than it really is.

I also know that the sum of the potential differences around a closed path are equal to zero, but I am not sure if this would help me. Help?

Solution:Using the equation E = deltaV/r, where r is the distance from the center of the square to each corner, you can calculate the electric field at the center. Since the square has a side length of 1 cm, r = 0.5 cm for each corner. For V1 and V2, the electric field is given by: E1 = (12.4 - 1.6)/0.5 = 11.2 V/cm For V2 and V3, the electric field is given by: E2 = (1.6 - 12.4)/0.5 = -10.8 V/cm For V3 and V4, the electric field is given by: E3 = (-9.2 - 1.6)/0.5 = -7.6 V/cm For V4 and V1, the electric field is given by: E4 = (1.6 - (-9.2))/0.5 = 10.8 V/cm The magnitude of the electric field at the center of the square is then the sum of all of these values, or 11.2 + 10.8 + -7.6 + 10.8 = 25.2 V/cm.

Hello! It looks like you're on the right track with your equations. To find the electric field at the center of the square, you can use the formula E = -∇V, where ∇ is the gradient operator and V is the electric potential. In this case, since the electric potential is given at each corner, you can calculate the gradient at each corner and then take the average to find the electric field at the center.

To do this, you can first calculate the differences in potential between each corner and the center. For example, at corner 1, the potential difference is V1 - Vcenter. Then, using the formula E = -∇V, you can find the electric field at each corner.

Once you have the electric field at each corner, you can take the average of these values to find the electric field at the center. This is because the electric field is a vector quantity, so you need to consider both the magnitude and direction at each point.

I hope this helps! Just remember to use the correct signs for the potential differences and to take the average of the electric field values at each corner. Good luck!

## 1. What is an electric field?

An electric field is a region in space where an electric charge experiences a force. It is created by a distribution of electric charges and can be either positive or negative.

## 2. How is electric field strength measured?

Electric field strength is measured in units of Newtons per Coulomb (N/C). This represents the amount of force per unit of charge experienced by an electric charge in the field.

## 3. What is electric potential?

Electric potential is the amount of work needed to move a unit of electric charge from one point to another in an electric field. It is measured in Volts (V).

## 4. How are electric field and electric potential related?

Electric potential is directly related to electric field. Electric field is the gradient of the electric potential. In other words, the electric field is the rate of change of electric potential with respect to distance.

## 5. Can electric field and electric potential be negative?

Yes, both electric field and electric potential can be negative. This indicates the direction of the force or work being opposite to the direction of the electric charge. However, it is important to note that electric potential is a scalar quantity, so it is the magnitude that is negative, not the quantity itself.

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