COULOMB’S LAW, E FIELDS
Class Activities
Coulomb’s Law
Class Activities:
Charge Distibutions
Two charges +Q and -Q are fixed a
distance r apart. The direction of the
force on a test charge -q at A is…
y
A.Up
B.Down
C.Left
D.Right
E.Some other direction,
or F =0
+Q
60
r
o
r
30o
r
-Q
.A
x
2.3
Two charges +q and -q are on the yaxis, symmetric about the origin. Point
A is an empty point in space on the xaxis. The direction of the E field at A
y
is…
+q
A. Up
A
B. Down
x
C.Left
-q
D.Right
E. Some other direction, or E = 0, or ambiguous
2.1b
How is the vector
Â12 related to r1 and r2?
Â12
r1
r2
A) Â12 = r1 + r2
B) Â12 = r1 - r2
C) Â12 = r2 - r1
D) None of these
kq1q2
Coulomb's law: F(by 1 on 2) =
Â̂12
2
Â12
In the fig, q1 and q2 are 2 m apart.
Which arrow can represent
ˆ ?
Â12
A
q1
B
q2
C
D) More than one (or NONE) of the above
E) You can't decide until you know if q1 and q2
are the same or opposite signed charges
2.2
What is Â̂1 ("from 1 to the point r") here?
r1=(x1,y1)
Â1 = r - r1
-q
+q
r=(x,y)
ˆ
A = A/ | A |
A) (x - x1 , y - y1 )
C)
B) (x1 - x, y1 - y)
(x - x1 , y - y1 )
(x - x ) + (y - y )
2
1
E) None of these
1
2
D)
(x1 - x, y1 - y)
(x - x ) + (y - y )
2
1
1
2
Only click when you are DONE with page 1
(Part 1 i-iii)
Is the answer to part 1- iii
A) A sum?
B) An integral over dy?
C) An integral over something else?
Tutorial 1, part 2- Script r
Only after you finish Part 2, what is
A) (x - x ', y - y ',z - z ')
C)
D)
B) (x '- x, y '- y,z '- z)
(x - x ', y - y ',z - z ')
( x - x ' ) + ( y - y ') + ( z - z ' )
2
2
2
(x '- x, y '- y,z '- z)
( x - x ') + ( y - y ') + ( z - z ')
2
E) None of these!
2
Â̂ in part 2-iv ?
2
2.5
5 charges, q, are arranged in a
regular pentagon, as shown.
What is the E field at the center?
q
q
q
A) Zero
q
q
B) Non-zero
C) Really need trig and a calculator to
decide
2.6
1 of the 5 charges has been removed, as
shown. What’s the E field at the center?
q
a
q
+y
A) +(kq/a2) j
+x
q
q
B) -(kq/a2) j
C) 0
D) Something entirely different!
E) This is a nasty problem which I need more
time to solve
2.10
To find the E- field at P=(x,y,z) from a thin line
(uniform linear charge density ):
E=
1
4pe0
What is
ò
1 ˆ
 ldl'
2
Â
y
Â= Â
?
dl'
A) X
C)
B) y'
dl ' + x
2
2
D)
Â
r'
x + y'
2
2
E) Something completely different!!
r
x
P=(x,0,0)
2.11
E(r ) =
ò
l dl'
4 pe0Â
3
Â
y
dl'
Â
r'=
(0,y',0)
r
x
P=(x,0,0)
2.11
E(r ) =
ò
l dl'
3
Â
4 pe0Â
dy ' x
A) ò 3
x
dy ' x
B) ò 2
( x + y '2 ) 3 / 2
dy ' y '
C) ò 3
x
dy ' y '
D) ò 2
( x + y '2 ) 3 / 2
,so
l
Ex (x,0,0) =
…
ò
4pe0
y
dl'
Â
r'=
(0,y',0)
r
E ) Something else
x
P=(x,0,0)
2.12
To find the E- field at P from a thin
ring (radius R, uniform linear charge
density ):
1
1 ˆ
P=(0,0,z)
E=
 ldl'
ò
2
4pe0
C
Â
A
D
y
what is  ?
dl'
x
R
B
E) NONE of the arrows shown
correctly represents Â
2.13
To find the E- field at P from a thin
ring (radius a, uniform linear charge
density ):
1
1 ˆ
P=(0,0,z)
E=
Â
l
dl'
ò
2
4pe0
Â
y
what is  ?
dl'
a
A) a 2 + z 2
B) a
2
C) dl' +z
2
D) z
E) Something completely different!!
x
2.16
Griffiths p. 63 finds E a distance z from
a line segment with charge density :
E=
1
2l L
(0,0,z)
4pe 0 z z + L
2
2
k̂
x
-L
+L
What is the approx. form for E, if z>>L?
2l L
E=
× (...)
4pe 0
A) 0
B) 1
C) 1/z D) 1/z^2
E) None of these is remotely correct.
2.16
Griffiths p. 63 finds E a distance z from
a line segment with charge density :
E=
1
2l L
(0,0,z)
4pe 0 z z + L
2
2
k̂
x
-L
+L
What is the approx. form for E, if z<<L?
2l
E=
× (...)
4pe0
A) 0
B) 1
C) 1/z D) 1/z^2
E) None of these is remotely correct.
2.14
To find E at P from a negatively charged sphere
(radius R, uniform volume charge density ) using
E=
1
4pe0
ò
1
Â̂ r dt '
2
Â
what is  (given the small
volume element shown)?
(x’,y’,z’)
P=(x,y,z)
B
z
C
y
D) None of these
R
A
x
2.15
E=
A)
B)
C) 
1
4pe0
ò
1
1
Â̂ r dt 
 (....?)
2
Â
40
X,Y,Z 
 dxdydz


(X  x)  (Y  y)  (Z  z) 


2
2
2
 
X,Y,Z
2
2
2 3/2
(X

x)

(Y

y)

(Z

z)


X  x,Y  y,Z  z
(x,y,z)
P=(X,Y,Z)
z
y
dq
R
x
 dxdydz
 dxdydz


(X  x)  (Y  y)  (Z  z) 


X  x,Y  y,Z  z
D) 
 dxdydz E) None of these
2
2
2 3/2
(X  x)  (Y  y)  (Z  z) 
2
2
2
2.15
E=
A)
B)
C) 
1
4pe0
ò
1
1
Â̂ r dt 
 (....?)
2
Â
40
X,Y,Z 
 dxdydz
2
2
2 

(X  x)  (Y  y)  (Z  z) 


 
X,Y,Z
2
2
2 3/2
(X

x)

(Y

y)

(Z

z)


X  x,Y  y,Z  z
(x,y,z)
P=(X,Y,Z)
Âz
y
R
x
 dxdydz
 dxdydz


(X  x)  (Y  y)  (Z  z) 


X  x,Y  y,Z  z
D) 
 dxdydz E) None of these
2
2
2 3/2
(X  x)  (Y  y)  (Z  z) 
2
2
2