Electric Fields ond Dipoles - Proctice
1. The electricfield lines on theleft hove twicethe
seporotion of those on the right.
A. If the mognitude of the f ield at A is 40 N/C, whot
is the mognifude of the f orce on o proton at A?
F=
tE=(,6.1o''Xog)
=
oc tr= 6.rlxbl.N t
of
field at
B. Whqt the
r*ril\'.^".il;T;'A;S.;d"f .te) fe =+ rlf-=9og\
is
2.
mqqnitude
the
B?
The nucleus of o plutonium-239 otom contoins 94 protons. Assume thot the nucleus is a
spherewith radius 6.64 fm ond with the charge of the protons uniformly spreod through
the spher e. At the nucleus surfoce, whot are the mognitude ond direction (rodiolly inword
F=g=(
:m*gL
/l
(ry.
or outword)
t
r
of
A
a)-'tr
protons?
-rrl\
the electric field produced by the
q
\ /
E
3,07;lo\
l.'ur'lo#-l
c
3.
Two porticlas qreottoched to on xqxis: porticle 1of charge-2.OO, !O-7 Cat x = 6.00 cm,
porticle 2 of charge +2.OO , !O-7 C st x = 2l.O cm. AAidway between the particles, whqt is
their net electric field
-2al^L E,
in unit-vector notqtion?
(
6
,
O=.-O
[2 lt.Sc"n g
0o
.-*,
?,S''l
to *q-\e$F
A
or
9O St,C
\__rz^v-
J.So^
E --6,3g*tdq t
,.
0 e, rn^,.
4.
Two chorged porticles qre on the x oxis: 'q = '3.2O t lO{e C of x
-3.00 m ond g = 3.20 x tO-te C ot x = +3.00 m. Whqt arethe
=
to the positive direction of the
x oxis) of lhe net electric f ield produced ot point P ot y = 4.00 m?
mcAnitude ond direction (relotive
Y
tompr\{nG co-ncsl
€ --(:
=
:
(CE^t: qqoso +
3
*cose
(s sq. rolqp-1 € ro
"b'b /A
b
\s)
r{_- -!,39x\o'"gt
.S
Alsr,
5.
of electrons (a) ond protons (p)
exists on o circulqr orc of radius p = 2.00 cm, with ongles
An uneven orrongement
30.0",O?= 50.0o,0s = 30.0", ond 0a = 2O.O". Whqt
sre the mognitude ond direction (relative to the positive
direction of the x oxis) of the net electric field produced
Or =
k,iii{i=jlffio'. ,r-^
L
-"'dg)til.Y.l<,r;* ci*j
(9.00,'6',0\
€r= q, ls";;*
E*= F
r (oSrro
e'r, .v cos"o)
\\"'
ll- F.,
u-) =(e's$I€'Rrn
- \rso sin ri *srrrl3o"+shfrd
(r,oorroi.)t\ , AA,"
r_,
;
€'j=-3'81
3,q3'{d6
9 =to"tfu
tr
+{
1L.,40
EC-
llCtt
Exomples
I.
Of Finding Electric Fields With Integrotion
Key Eguotion:
e=Jae=Jf
If.
Problems
A. Uniformly Chorged Rod
1.
Lineqr chargedensity:
z.dq=
i =?
r9r
rn
Ldy. ,.,
3. Suggest o moteriol thot this rod could be mode
4. Find the electric field ot point
t-
€
J-
L
E=ldE = )(Kdj
rz
P.
from: Pla{ilf O
dx
-a
2l=
f\- k )"dx
)
-L
xt
=
\<r.fl dx
1z
k,l
TL
i=kl t
2L
*o r'Shf
B. Uniformly Charged Circulor Arc
1.
Lineor charge density:
n
fot"
=
I
= \dP
?-dq= ,\,dS
3. E =
a_
f = - -S,
Jae.ora
qnd
cl
rn
rcl
: o. why?
Jotr
\
y rornmn
Cqnc€{
er@
e
4.E =
Jae.ore
-e
= I"Y*"
=
-e
\
K\ttcose
rA
-@
KT
r
rQ
\
)
kr
r
cos ode
-9
(s ns ln
-9
kr (srn o stnt")
I
5rna
\-
When
9=O, E--O
o-'tY
J- - Jk}.
r- -E> c
T-
C. Uniformly Chorged Disk
1.
Surfoce charge density: o
z. d^=
=
rtr
rn'
-+-t=-
Qtlc d c
3. Find the aXeo of the circle
A = (an =
T0
using A
= [Oo
Iir"a. : irir (i;. =gfi lLr"
\-
4.dq=
q'dA
r.
r
5. Whqt is the direction of the electric field very nes? the surfqce of the disk?
disk is seen edge on it the figure below.)
6, Whqt is the direction of ihe electric field very for from the disk (i.e outside of the
dotted lines)?
n
I
I
J
1Td
D. Uniformly Charged Sphere
A nonconducting sphere of rodius R contqins q totql charge of
Q distributed uniformly throughout its volume (e.9. its volume
constont). O
1. Volume charg-e density: p = V
chargedensity p is
z. dv =
n .r.
4(YC'dc
Fin$fhe volume of the sphereusing v =
=
V= \dV=
$'lT'c"dr
^
9.
f
rn
t
Juv
4ffC.'lj t'iYn'
=
4 dc= PdV r.r
the enclosed charge
the totql chorge Q.
5. Whqt is
Q*doC
6. Whqt is
=
Qenctosed
(i.e.
the charge inside the rodius r)
in terms of
I^r3
(ila
the magnitude of the electric field ot o rodi us r when r 4P in terms of the
totol chorge Q?
=K"
ryr'*'".'@
t
\^'
LJ
l_
R3
7. Whqt is the magnitude of the electricfield ot o rodius r when r4n
'
in terms
of the
chorge density p ?
Y,'L.G
pe
=k'+fi.=g
pa
Ass r
3
Whot is the mcgnifude of the electric field ot o rodius r when r)R?
€r- --kc.
y;z
rr
9. Drqw the groph
E
of- E versus r thct includes the field both the inside ond outside.
Hl"i)