Finding the Electric Field Zero Point: A Point Charge Problem

[Haythamgg]

Homework Statement

A point charge of -2 micro coulomb is located at the origin ,a second charge point of 6 micro coulomb is at x= 1m and y= 0.5 m
Find the x and y coordinates of the position where the electric field is zero

Homework Equations

E=κq/ r^2 multiplied by unit vector

The Attempt at a Solution

 

[AJ Bentley]

You need to show us you've at least tried to solve it!

 

[Haythamgg]

I supposed that there is another point (p) where the electric field is zero
E1+E2=0
E1= kq1/r1^2 *unit vector
E2 = kq2/r2^2 * unit vector then tried to solve them but there is many unknown

 

[AJ Bentley]

There's something else you can say about the point where the field is zero. It must be somewhere on a straight line between the two charges.
So how can you work out exactly where? (The field from each charge falls off as the square of the distance.)

Make a diagram. Draw the two charges, then draw a line between them. Mark a point on that line and call it the zero point. At that point, the field from each charge will be exactly equal and opposite so you can use the 1/r² law to work out where it is.
After that it's just a bit of Pythagoras to work out the co-ordinates.

 

[Haythamgg]

How can I use the inverse law if I don't have the distance of both

 

[AJ Bentley]

Call the distance from the point to the first charge R1, call the distance to the second R2.
Then R1 + R2 is the total distance between the charges and 2/R1² = 6/R2² from the inverse square law.
Two equations, two unknowns so you have a pair of simultaneous equations to work out what R1 and R2 must be.

 

[Haythamgg]

Ok now I've got the distanace now i need the x and y coordinates