# Electric field at a point on a contour line

• maxsthekat
In summary, the question asks to calculate the size of the electric field at point k, with the image provided showing the contour lines in kV. The equation used is ∆V = Ed and the attempt at a solution involves setting V = -5kV and measuring the distance from point k to Q1. The suggestion is to measure the perpendicular distance from k to the nearest contour line and express E as a certain number of volts per meter.

#### maxsthekat

Hi guys!

In this question I am asked to "Calculate the size of the electric field at k". See image at: http://capa-new.colorado.edu/msuphysicslib/Graphics/Gtype54/prob04a_threeqcontour.gif

Note: although the picture states "Volts", everything is actually measured in kV.

∆V = Ed

## The Attempt at a Solution

I tried to set V = -5kV, and solving for E by measuring the distance from point k to Q1, but this doesn't seem to work. Will I have to do this for all three charges? Or, am I totally off base and should be approaching it from a different angle?

-Max

maxsthekat said:
Hi guys!

In this question I am asked to "Calculate the size of the electric field at k". See image at: http://capa-new.colorado.edu/msuphysicslib/Graphics/Gtype54/prob04a_threeqcontour.gif

Note: although the picture states "Volts", everything is actually measured in kV.

∆V = Ed

## The Attempt at a Solution

I tried to set V = -5kV, and solving for E by measuring the distance from point k to Q1, but this doesn't seem to work. Will I have to do this for all three charges? Or, am I totally off base and should be approaching it from a different angle?

-Max

As I figure it the difference between each contour line is 1 KV. Since

$$E = -\frac{\Delta V}{d}$$

you want to measure the perpendicular distance from k to the nearest contour line and express E as so many volts per meter (or what ever distance unit you desire). Note the minus sign in my equation. That implies something about the direction of E.

Hello Max,

In order to accurately calculate the size of the electric field at point k, you will need to take into account the contributions from all three charges (Q1, Q2, Q3) as they all have an influence on the electric field at that point. Simply measuring the distance from point k to Q1 will not give you an accurate result.

One approach you could take is to use the formula for electric field due to a point charge, which is E = kQ/r^2, where k is the Coulomb's constant, Q is the charge, and r is the distance between the point charge and the point at which the electric field is being calculated. You will need to calculate the electric field contribution from each charge separately and then add them together to get the total electric field at point k.

Another approach could be to use the superposition principle, which states that the total electric field at a point is the vector sum of the individual electric fields due to each charge. This means you would need to calculate the electric field at point k from each charge separately, taking into account the direction and magnitude of each field, and then add them together to get the total electric field at point k.

I hope this helps! Good luck with your calculations.

Best,

## 1. What is an electric field at a point on a contour line?

The electric field at a point on a contour line is a vector quantity that represents the strength and direction of the electric field at that specific point on the contour line.

## 2. How is the electric field calculated at a point on a contour line?

The electric field at a point on a contour line is calculated using Coulomb's Law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charge and the point on the contour line.

## 3. What factors affect the electric field at a point on a contour line?

The electric field at a point on a contour line is affected by the magnitude and direction of the charge, as well as the distance between the charge and the point on the contour line. Additionally, the presence of other charges and the medium between the charge and the point can also affect the electric field.

## 4. How does the electric field vary along a contour line?

The electric field may vary along a contour line depending on the distribution of charges and the shape of the contour line. In general, the electric field will be strongest at points closest to the charge and will decrease as the distance from the charge increases.

## 5. How is the electric field represented on a contour map?

The electric field at a point on a contour line is typically represented by the direction and length of the arrows on a contour map. The direction of the arrow indicates the direction of the electric field, while the length represents the strength of the field at that point.