 #1
ISAZI
 2
 0
 Homework Statement:
 Help with Electric field homework
 Relevant Equations:

E⃗ =
Q2ϵ0L2i^
Charge QQ is uniformly distributed along a thin, flexible rod of length LL. The rod is then bent into the semicircle shown in the figure (Figure 1).
Find an expression for the electric field E⃗ E→ at the center of the semicircle.
Hint: A small piece of arc length ΔsΔs spans a small angle Δθ=ΔsΔθ=Δs /R/R, where RR is the radius.
Express your answer in terms of the variables QQQ, LLL, unit vectors i^i^i_unit, j^j^j_unit, and appropriate constants.
I really don't even know where to start here as there really isn't a lecture in this course.
I know that
electric field= q/r^2
so my first though was to rewrite R using arc length. Then I realized arc length won't really help. so I figured I had to write the formula in away that accounts for the radius at any given point or so I thought.
I know there's a really long formula1/4piepisolon * q/r^2 cos theta which could be written as xq/(x^2+d^2)^3/2. I know I have to think about the question carefully but I'm lost so I was wondering if somebody could help me understand better what it is that I'm trying to find and how I can think about the question and come to the conclusion. I already have the answer but its the path to the answer that I'm searching
Find an expression for the electric field E⃗ E→ at the center of the semicircle.
Hint: A small piece of arc length ΔsΔs spans a small angle Δθ=ΔsΔθ=Δs /R/R, where RR is the radius.
Express your answer in terms of the variables QQQ, LLL, unit vectors i^i^i_unit, j^j^j_unit, and appropriate constants.
I really don't even know where to start here as there really isn't a lecture in this course.
I know that
electric field= q/r^2
so my first though was to rewrite R using arc length. Then I realized arc length won't really help. so I figured I had to write the formula in away that accounts for the radius at any given point or so I thought.
I know there's a really long formula1/4piepisolon * q/r^2 cos theta which could be written as xq/(x^2+d^2)^3/2. I know I have to think about the question carefully but I'm lost so I was wondering if somebody could help me understand better what it is that I'm trying to find and how I can think about the question and come to the conclusion. I already have the answer but its the path to the answer that I'm searching