Classical Dynamics of Particles and Systems · Problem 1-36

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · surface-integrals

Problem

Find the value of the integral

\int_S \mathbf{A} \cdot d\mathbf{a}

, where

\mathbf{A} = x\mathbf{i} - y\mathbf{j} + z\mathbf{k}

and

S

is the closed surface defined by the cylinder

c^2 = x^2 + y^2

. The top and bottom of the cylinder are at

z = d

and 0, respectively.