Calculating Electric Field at a Given Position Due to a π- Particle

[Squall]

Homework Statement

A π- ("pi-minus") particle, which has charge -e, is at location ‹ 5.00e-9, -5.00e-9, -6.00e-9 › m. What is the electric field at location < -5.00e-9, 3.00e-9, 5.00e-9 > m, due to the π- particle?
5e-9 is equivalent to 5*10^-9

Homework Equations

E=(k*q/r^2)r-hat

The Attempt at a Solution

So to find the Electric field created at the given position first I subtract the source from the observation, I am assuming the pi- particle is the source. When I do this is what I get
<-10e-9,8e-9,11e-9>

So next I compute the r^2 or the distance from source to observation location. To do this I square each entry in the vector above and add them up to get 8.5e-17

Now I compute the value to the left of the r-hat vector: 9e9*(-1.602e-19/8.5e-17), this gives me -16962352.94 N/C

Next I calculate the r-hat vector by dividing r by its magnitude which is sqrt(8.5e-17).
I get <-1.0846, .8677, 1.1931>

[-16962352.94 N/C *<-1.0846, .8677, 1.1931>]
Finally I multiply the two numbers together and get a vector with huge values, which doesn't seem right, can some one tell me where I am going wrong or maybe tell me the right way to approach this problem, because I seem to be stuck.
Thank You for your help.

 

[gneill]

Your value for |r|² looks dubious. Better check it.

 

[Squall]

Yes the |r|^2 was dubious

After reworking that I got |r|=1.6882e-8

Plugging this back in I get
E=[9e9*(1.602e-19)/(1.6882e-8)^2]*< -0.5923, 0.4739, 0.6516>

=<2996700,-2397300,-3296300>

Is this a more reasonable answer?

 

[gneill]

The results look good.

You might want to use scientific notation and appropriate significant figures for your final answer.

 

[rwisz]

Your approach is correct, but there are a few errors in your calculations. First, when you subtract the source from the observation, your result should be < -1.0e-8, 8.0e-9, 11.0e-9 > m, not < -10e-9, 8e-9, 11e-9 > m. This is because you are subtracting the coordinates of the source from the coordinates of the observation, not the other way around.

Secondly, when you calculate the magnitude of the displacement vector (r), you should get 1.3e-8 m, not 8.5e-17 m. This is because you need to take the square root of the sum of the squares of the components of the displacement vector, not the displacement vector itself.

Finally, when you calculate the electric field using the formula E = (k*q/r^2)r-hat, you should get a vector with values of -1.3e8 N/C, 1.0e8 N/C, and 1.4e8 N/C for the x, y, and z components respectively.

I hope this helps clarify the problem for you. Keep in mind to always double check your calculations and make sure you are using the correct units. Good luck with your studies!