# Vector Fields

1. Nov 23, 2008

### withthemotive

1. The problem statement, all variables and given/known data

Find the work done by the force field F(x, y, z) = 3xi +3yj + 7k on a particle that moves along the helix r(t) = 4 cos(t)i + 4 sin(t)j + 4tk, 0 ≤ t ≤ 2π (As in the previous problem, recall that the work of the force F on the helix corresponds to the circulation of this vector field along the curve).

2. Relevant equations

3. The attempt at a solution

F(x, y, z) = 3xi +3yj + 7k
r(t) = 4 cos(t)i + 4 sin(t)j + 4tk , 0 ≤ t ≤ 2π
r'(t) = -4sin(t)i + 4cos(t)j + 4

$$\int$$F(dot)dr
$$\int$$(-48cos(t)sin(t) + 48cos(t)sin(t) + 28)dt
$$\int$$ (28)dt

With the integral going from 0 to 2pi I thought the answer would be 48pi, but it's not.

2. Nov 23, 2008

### withthemotive

Nevermind, I got it, it's 28*2pi