Find the coordinates of a charged particle given the E field

[Curtis Cleary]

Homework Statement

The electric field in an xy plane produced by a positively chatged particle is 7.2(4x+3y)N/C at the point (3, 3)cm and 100x N/C at the poiint (2, 0)cm. Note, x and y used here are unit vectors.

1. find the x and y co-ordinate of the charged particle
2. what is the charge of the particle?

Homework Equations

E=Q/4πε₀r²

The Attempt at a Solution

I tried using the above formula for the two points given to no avail and becomes very messy.
I've tried using the formula for a electric field and equating it at the two points given but it doesn't give me the co-ordinates of the charge. Any help would be most appreciated.

for point 1, i set E=Q/4πε₀r²=|28.8x+21.6y|=36, therefore Q=144πε₀((x-3)²+(y-3)²)

Then for point 2, Q=400πε₀((x-2)² +y²)

Equating them we have (x-3)² +(y-3)²=25/9((x-2)² +y²)

And then expanding we get x² +y² -(23/8)x+(27/8)y - 31/8 = 0

This is an equation of a circle so I don't understand how we can find the co-ordinates of the point :(

 

[Orodruin]

I tried using the above formula for the two points given to no avail and becomes very messy

Please type out your work. Not only is this required by the homework guidelines, it is also impossible for us to tell where you go wrong if you do not.

 

[Curtis Cleary]

Please type out your work. Not only is this required by the homework guidelines, it is also impossible for us to tell where you go wrong if you do not.

Hello, I've now wrote out what I've done so far and hopefully you may see where I've went wrong, thank you for your help

 

[Orodruin]

You have only used information about the magnitude of the field, but you also have information about the direction. Can you find a way to use the directional information to deduce where the charge is?

 

[Curtis Cleary]

You have only used information about the magnitude of the field, but you also have information about the direction. Can you find a way to use the directional information to deduce where the charge is?

Ah, I think I've got it. At point 2 that's given the Electric field only has an x component which means since the electric field produced by the charge is radial, it must have the same y-coordinate as point 2, then i can use the equation i derived to find the x co-ordinate, is my thinking correct?

 

[Orodruin]

That is one way of doing it. You could also use a similar argumentation about the direction of the field at point 1 (which will give you another line - you will then have two lines on which the charge has to be, how can you find the position of the charge based on that?). The two methods should give the same answer (or the problem is not well constructed).