Magnitude and direction of electric force (file attached)

[trah22]

Homework Statement

I was kind of confused on how the radius for the charge on q3 by q1 is 2a^2, i attached the file for my notes regarding this. The question is at the bottom of the pdf scan.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

The needed distance is the hypotenuse of the right triangle whose sides are both "a". Hint: Pythagorean theorem.

 

[trah22]

c^2=a^2+b^2

so

c^2=a^2+a^2
c^2=2a^2

what about the ^2 for the c, is it just left there? because it seems like it since r=2a^2

 

[Doc Al]

Careful: it's r^2 = 2a^2, not r = 2a^2.

 

[trah22]

On this other page of notes which has to do with the introduction of acceleration in electric fields, there are three parts of the problem that I am not quite following, i figured it would be easier if i just wrote it down by hand on the actual note sheet than typing it all out.

For the cosign question, i don't undestand what happened to it because the sin is still there in the next step but not the cos.

 

[trah22]

If what I am asking isn't really quite clear, i can write it out again more specifically and scan it.

 

[Doc Al]

(Be sure to include the full problem statement next time.)

(1) Why negative? The field points down (thus is negative), the charge is positive: so the force and acceleration are both downward, thus negative.

(2) They are solving for the value of time that makes y = 0. Set that factor equal to zero and solve for t.

(3) Regarding what happened to the cosine: note that $\theta$ changed to $2\theta$. (Review your trig identities for $\sin\theta \cos\theta$.)