Question

any energy expended in moving (raising) an ob
ject against the field is recovered exactly when
the object is returned (lowered) to its original
position. Anonconservative gravitational field
could solve our energy problems forever.
Given a nonconservative field, it is of
course possible that the line integral may be
zero for certain closed paths. For example, con
sider the force field, F=sinpas. Around a cir
Figure 4.4 A simple de circuit problem that must
cular path of radius p=e, we have dead be solved by applying Yeo-o in the form of
Kirchholl's voltage law
$7.01-sin doa, - a sin de
2 mp, sin
and
The integral is zero if p=1,2,3,..., etc., but it is not vero for other values of pior for mos
her closed paths, and the given field is not conservative. A conservative field must yield a zeu
lue for the line integral around every possible closed path
D4.6. If we take the zero reference for potential at infinity, find the potential at (0, 0, 2) cause
by this charge configuration in free space (a) 12 nC/m on the line p 2.5m, 20; (b) point char
of 18 nCat (1, 2, -1); (c) 12 nC/m on the line y-2.5.20. -1.0<x<1.0.
Ans.(a) 529 V: (b) 43.2 V: (c) 66.3 V​

Answer 1

any energy expended in moving (raising) an ob

ject against the field is recovered exactly when

the object is returned (lowered) to its original

position. Anonconservative gravitational field

could solve our energy problems forever.

Given a nonconservative field, it is of

course possible that the line integral may be

zero for certain closed paths. For example, con

sider the force field, F=sinpas. Around a cir

Figure 4.4 A simple de circuit problem that must

cular path of radius p=e, we have dead be solved by applying Yeo-o in the form of

Kirchholl's voltage law

$7.01-sin doa, - a sin de

2 mp, sin

and

The integral is zero if p=1,2,3,..., etc., but it is not vero for other values of pior for mos

her closed paths, and the given field is not conservative. A conservative field must yield a zeu

lue for the line integral around every possible closed path

D4.6. If we take the zero reference for potential at infinity, find the potential at (0, 0, 2) cause

by this charge configuration in free space (a) 12 nC/m on the line p 2.5m, 20; (b) point char

of 18 nCat (1, 2, -1); (c) 12 nC/m on the line y-2.5.20. -1.0<x<1.0.

Ans.(a) 529 V: (b) 43.2 V: (c) 66.3 V