Electric field at a point on a contour line

[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.

Homework Equations

∆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?

Thanks for your help!

-Max

 

[AEM]

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.

Homework Equations

∆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?

Thanks for your help!

-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.

 

[nlightner]

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,