# Thread: Vector Calculus - Line integrals

1. ## Vector Calculus - Line integrals

I have a question from a problem sheet which I've been struggling with for some time now so I thought I'd post here to get some help.

A circular piece of wire of radius 1m in the xy plane, centred at the origin has a mass (kg) per unit length given by ϕ=3+x+y. Calculate the total mass of the wire.

2. ## Re: Vector Calculus - Line integrals

Hey TarSha.

Your integral will be adding up all the infinitesimal dm portions of the wire. Try using the projection of the mass at x,y against the the circle centred at (0,0) with radius.

Hint: The projection will be based on the inner product and use the standard parameterization of the circle (sin(t),cos(t))

3. ## Re: Vector Calculus - Line integrals

The mass of a small piece (with central angle $\displaystyle d\theta$) would be $\displaystyle \phi rd\theta$. So you substitute $\displaystyle \phi=3+r\cos{\theta}+r\sin{\theta}$ and integrate from 0 to $\displaystyle 2\pi$.

- Hollywood