Calculating Electric Field from a Bent Rod of Charge

[musicfairy]

A rod of uniform linear charge density λ = +1.5 x 10 5 C/m is bent into an arc of radius R = 0.10 m. The arc is placed with its center at the origin of the axes shown above.
a. Determine the total charge on the rod.
b. Determine the magnitude and direction of the electric field at the center O of the arc.

A proton is now placed at point O and held in place. Ignore the effects of gravity in the rest of this problem.
d. Determine the magnitude and direction of the force that must be applied in order to keep the proton at rest.

My work for part a:

Got this part right.

For part b:

Didn't get this one right. I got 46722.8 for the answer while the correct answer is 2.3 × 10⁶

What did I do wrong?

For part d I need the answer from part b. If I had it I would use F = qE.

I don't understand part e at all.

Please help me, especially on part b.

 

[Doc Al]

Didn't get this one right. I got 46722.8 for the answer while the correct answer is 2.3 × 10⁶

What did I do wrong?

All I see wrong is a missing factor of R in your final answer. I assume that λ = 1.5 x 10^-5 C/m. If so, the correct answer follows.

 

[musicfairy]

I got it. Thanks.