# 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!

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