Three Point Charges in a Row, Find Magnitude 1.5cm left of middle charge

fal01

1. The problem statement, all variables and given/known data
Consider three charges arranged as shown.

+ + -
1 2 3
What is the magnitude of the electric field
strength at a point 1.5 cm to the left of the
middle charge? The value of the Coulomb
constant is 8.98755 × 10^9N
m2/C2.
Answer in units of N/C

q1=8.2 µC= 8.2*10^-6 C
q2=4.5 µC = 4.5*10^-6 C
q3=−4 µC= -4*10^-6 C

r1,2=4.4 cm= .044m
r2,3= 4.6 cm=.046m

kC= 8.98755*10^9

2. Relevant equations

F=kC*q1q2/r^2

3. The attempt at a solution

so I am guessing I need to start off with something like this...

F2,1=kC*q2q1/r2,3^s

F2,3= kC * q2q1/r2,3^2

and then find Fnet= F2,1 +F2,3

One of the main things I am struggling with is the 1.5cm (.015m) left of the center point.

davo789

You said in the original question that you wanted to find the electric field, but then started trying to calculate the force! I think the reason you're struggling is because you can't calculate the force of charges on a bit of chargeless space. Your logic is fairly sound otherwise!

fal01

Oh lol...

Then I use E=F/q=kq/r^2

then do I calculate the E for each one?
like so..


E1=k*q1/r^2
E2=k*q2/r^2
E3=k*q3/r^2

then what would r be?

davo789

What do you think r would be?

fal01

I am guessing the r should be different for each one...

E1=k*q1/r^2 r=.044m -.015m=.029m
E2=k*q2/r^2 r=.015m
E3=k*q3/r^2 r=.046m +.015m=.061m

davo789

Yes, exactly that!

fal01

So now
E1=8.76*10^7
E2=1.8*10^8
E3=9.66*10^6

so, Enet=E1-E2+E3

Did I get the signs right?

davo789

Yes, good spot!

fal01

Thanks so much! I got it! :)