Question

What is the correct answer to this question?

Find the work done by the force field

F(x,y,z) = -x^2y^3 i + 4 j + x k

acting on a charged electric particle moving along a path given by the equation

r(t) = 2cost i + 2 sint j +4 k

where the parameter t varies from pi/4 to 7pi/4

Answer 1

F = -32cos^2(t)sin^3(t)i + 4j + (2cost)k

integrate fdr

now dr -> (dr/dt) * dt

so dr/dt is the derivative of r(t) :
dr/dt = v(t) = -2sinti + 2costj

put all together :

f * (dr/dt) * dt

Answer 2

and integrate..

Answer 3

Thanks for your help.

Answer 4

you are welcome :)