Three Point Charges, find the electric force exerted

[m00nbeam360]

Homework Statement

Three charges, each of magnitude 2 nC, are at separate corners of a square of edge length 1 cm. The two charges at opposite corners are positive, and the other charge is negative. Find the force exerted by these charges on a fourth charge q = +3 nC at the remaining (upper right) corner. (Assume the +x axis is directed to the right and the +y axis is directed upward.)

Homework Equations

k = (8.988*10^9 N*m^2/C^2)

The Attempt at a Solution

Drew a diagram of the problem such that F4 = F1,4 + F2,4 + F 3,4.

F1,4 = (k*q1*q4)/(r(1,4)^2)j

F1,4 = (8.988*10^9 N*m^2/C^2)(2.00*10^-9)*((2.00*10^-9)/(0.01m)^2)

= 3.595 * 10^-4 j

F2,4 = same

F3,4 = (k*q1*q2)/(r(2,4)^2)*r(3,4)

r(3,4) = r(3,1) + r(1,4) = (0.01m)i + (0.01m)j

r(3,4) = (0.01m)i+(0.01m)j/(sqrt(0.01m^2+0.01m^2)) = 0.14i + 0.14j

F3,4 = (8.988*10^9) (-2.00*10^-9)(2.00*10^-9)/(0.01sqrt(2)^2)*(0.14i+0.14j)

= -2.52 * 10 ^ -5

(3.595 * 10^-4) i - (-2.52*10^-5) i = 3.34*10^-4i <--- Wrong :(
(3.595 * 10^-4) j - (-2.52*10^-5) j = 3.34*10^-4j <--- Wrong :(


Any suggestions?? I think that somewhere in computing F3,4 I put in an incorrect number. Thanks!

 

[TSny]

r(3,4) = (0.01m)i+(0.01m)j/(sqrt(0.01m^2+0.01m^2)) = 0.14i + 0.14j

Check this.

 

[m00nbeam360]

Whoa, got .707 now, thanks. So then is everything else correct?

 

[TSny]

F1,4 = (k*q1*q4)/(r(1,4)^2)j

F1,4 = (8.988*10^9 N*m^2/C^2)(2.00*10^-9)*((2.00*10^-9)/(0.01m)^2)

= 3.595 * 10^-4 j

Did you use the correct value for q4 here?

 

[Nickie]

Your attempt at solving the problem is correct. The mistake may be in your calculations. Make sure to check your units and that you are using the correct values for the charges and distances. Also, double check your calculations for F1,4 and F2,4. If the problem persists, try solving the problem again and see if you get the same answer. If not, you may need to seek help from a classmate or your instructor.