1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Nonuniformly charged semicircle

  1. Jan 24, 2010 #1
    A non-uniformly charged semicircle of radius R=18.5 cm lies in the xy plane, centered at the origin, as shown. The charge density varies as the angle θ (in radians) according to λ = − 4.42 θ, where λ has units of μC/m.What is the total charge on the semicircle?

    2. Relevant equations: Q=(lambda)/L, L=(theta)*radius

    I calculate Q to be (lambda)*L, or Q=(-4.42*(theta))*(.185*(theta)). I then ran this over the integral from theta=zero to theta=(pi). I got an answer in micro-Coulombs so I converted it to Coulombs to answer. I ended up with -8.4513E10^-6, but it says that It's incorrect...help!?!?! due at 11 tonight!
  2. jcsd
  3. Jan 24, 2010 #2

    You know that a very small section of the charge would be dQ. You also know that the charge Q = (lamda)*s (this was wrong under your relevant equations (the arc length of that segment)). So... dQ = (lamda)*ds using some basic trig and what not you know that ds = r*d(theta) so then you get...

    dQ = lamda*R*dTHETA and you're give your value of lambda so sub that in and you get...

    dQ = -4.42(Theta)*R*d(theta) so integrate with respect to theta from 0 to pi b/c it's a semi-circle so you get...

    Q = -4.42*R[ integral from 0 to pit of (theta d theta) ]


    q = -4.42*R*(theta)^2/2 from 0 to pi...

    Hope this helps :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Nonuniformly charged semicircle Date
Calculate net charge with nonuniform electric field Sep 4, 2016
Nonuniform Rod Electric Field Jan 27, 2016
Nonuniform Semicircle of Charge Jan 24, 2012
Nonuniform Semicircle of Charge problem Jan 15, 2010
Nonuniformly Charged Semicircle Sep 3, 2009