Semicircular Wire (Couloumb's law)

1. Oct 20, 2012

Fabio010

Semicircular Wire
A positively charged wire is bent into a semicircle of radius R, as shown in Figure 2.15.4.

The total charge on the semicircle is Q. However, the charge per unit length along the
semicircle is non-uniform and given by

λ = λo θ cos .

(a) What is the relationship betweenλo , R and Q?

(b) If a charge q is placed at the origin, what is the total force on the charge?

Attempts:

a)

dq = λdl = λRdθ

dq = λo.cosθ.R.dθ

Q = ∫(-pi/2 to pi/2) [λo.cosθ.R.dθ]

Q = 2λoR

b)

Force in x axis = ((Ke.q.λo.cosθ.R.dθ)/(R^2))*sinθ integrating that in order to dθ, the result is zero.

Force in y axis = ((Ke.q.λo.cosθ.R.dθ)/(R^2))*cosθ integrating that in order to dθ, the result is (Ke.q.λo/R)*(0.5*pi)

Is that correct??

Last edited: Oct 20, 2012
2. Oct 20, 2012

TSny

Bingo! Good work.

3. Oct 21, 2012

Staff: Mentor

To make your professor happy, you should solve for λ0 in terms of Q, and substitute that into your final answer.

4. Oct 22, 2012

Fabio010

lol ok thanks for the help!