I just want to give you credit for your last statement in the original post that your guess that v=gt factors in the acceleration but v=d/t does not is absolutely correct.
Thanks for the input, Choppy. The tricky thing about your first question is it's really a combination of both. I've had a deep rooted desire to pursue physics since I graduated and only took the job I have now to pay for my last year of college and be able to more easily support my family as I...
I graduated in 2016 with my Physics BS and Electronics Engineering BS. Ever since I started the physics major I knew I wanted to go into a research and development job like at a lab. Not really interested in being a teacher except maybe college since professors have opportunities for doing their...
Thanks, Delta2. I guess I should have tried to work it out using Gauss' Law before even posting. For the total bound charge, I got ##Q=-4\pi \alpha r^{n+2} +4\pi \alpha a^{n+2}## which makes sense since when r=a to find the total charge, Q=0 since the sphere should be neutral.
Then to find the...
Solving for the volume and surface bound charge densities was easy using equations 1) and 2).
The polarization only has an r component so
##ρ_b=-\frac 1 {r^2} \frac {d} {dr} (r^2 \vec P)=-α(n+2)r^{n-1}##,
and ##\hat n=\hat r## so
##σ_b=αa^n##.
To find ##\vec E## I intend to use equation 3)...