CHAPTER 5 VECTOR INTEGRATION INTEGRAL THEOREMS AND Example 5.6 2xy iˆ a) Show that 3xz is a conservative force field. F   z  x  ˆj 3 2 2kˆ b) Find the scalar potential. c) Find the work done in moving an object in this field from (1,-2,1) to (3,1,4). a) is conservative if 0   F F i j k    0 F 2xy 2  z x 3 2 Hence is conservative. F b)   k ˆ ˆ F      F d r dx dy  3 2 2        const. 2 3 x,    y, z x y xz const. 2 3 Work done  202 P2 P1 3,1,4 59
CHAPTER 5 VECTOR INTEGRATION AND INTEGRAL THEOREMS Example 5.6 a) Show that F  2xy  z 3 iˆ  x 2 ˆj  3xz 2kˆ is a conservative force field. b) Find the scalar potential. c) Find the work done in moving an object in this field from (1,-2,1) to (3,1,4). a) F is conservative if  F  0 i j k  F   0 2xy  z 3 x 2 2 Hence F is conservative. b) F   ˆ  ˆ  k F  d r  dx  dy  3 2 2        const. 2 3 x, y, z  x 2 y  xz 3  const. Work done  202 P2 P1 3,1,4 59