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COULOMB S LAW, E FIELDS - University of Colorado …s law: In the fig, q1 and q2 are 2 m apart....
Transcript of COULOMB S LAW, E FIELDS - University of Colorado …s law: In the fig, q1 and q2 are 2 m apart....
![Page 1: COULOMB S LAW, E FIELDS - University of Colorado …s law: In the fig, q1 and q2 are 2 m apart. Which arrow can represent ? F(by 1 on 2) = kq 1 q 2 Â 12 2 Â Ö 12 Â Ö 12 q1 q2](https://reader031.fdocuments.in/reader031/viewer/2022030417/5aa32f7b7f8b9aa0108e3c7b/html5/thumbnails/1.jpg)
COULOMB’S LAW, E FIELDS
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Class Activities
Coulomb’s Law
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Class Activities:
Charge Distibutions
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Two charges +Q and -Q are fixed a
distance r apart. The direction of the
force on a test charge -q at A is…
A.Up
B.Down
C.Left
D.Right
E.Some other direction,
or F =0
. A
+Q
-Q
r
r
r
x
y
60o
30o
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Two charges +q and -q are on the y-
axis, symmetric about the origin. Point
A is an empty point in space on the x-
axis. The direction of the E field at A
is…
A.Up
B.Down
C.Left
D.Right
E.Some other direction, or E = 0, or ambiguous
2.3
+q
x
y
-q
A
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How is the vector related to r1 and r2? 12Â
r2
r1
12Â
12 1 2
12 1 2
12 2 1
A) r r
B) r r
C) r r
D) None of these
 = +
 = -
 = -
2.1b
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Coulomb's law:
In the fig, q1 and q2 are 2 m apart.
Which arrow can represent ?
F(by 1 on 2) =
kq1q2
Â12
2 Â̂12
ˆ Â 12
q1 q2
A
B 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
![Page 8: COULOMB S LAW, E FIELDS - University of Colorado …s law: In the fig, q1 and q2 are 2 m apart. Which arrow can represent ? F(by 1 on 2) = kq 1 q 2 Â 12 2 Â Ö 12 Â Ö 12 q1 q2](https://reader031.fdocuments.in/reader031/viewer/2022030417/5aa32f7b7f8b9aa0108e3c7b/html5/thumbnails/8.jpg)
What is ("from 1 to the point r") here?
+q
r1=(x1,y1) -q
r=(x,y)
Â̂1
Â1 = r - r1
ˆ A =
A / | A |
2.2
A) (x - x1, y - y
1) B) (x
1- x, y
1- y)
C)(x - x
1, y - y
1)
x - x1( )
2
+ y - y1( )
2D)
(x1- x, y
1- y)
x - x1( )
2
+ y - y1( )
2
E) None of these
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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?
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Tutorial 1, part 2- Script r
Only after you finish Part 2, what is in part 2-iv ?
Â̂
A) (x - x ', y - y ',z - z ') B) (x '- x, y '- y,z '- z)
C)(x - x ', y - y ',z - z ')
x - x '( )2
+ y - y '( )2
+ z - z '( )2
D)(x '- x, y '- y,z '- z)
x - x '( )2
+ y - y '( )2
+ z - z '( )2
E) None of these!
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5 charges, q, are arranged in a
regular pentagon, as shown.
What is the E field at the center?
A) Zero
B) Non-zero
C) Really need trig and a calculator to decide
q
q
q q
q
2.5
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1 of the 5 charges has been removed, as
shown. What’s the E field at the center?
q
q q
q
A) +(kq/a2) j
B) -(kq/a2) j
C) 0
D) Something entirely different!
E) This is a nasty problem which I need more time to solve
+x
+y a
2.6
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To find the E- field at P=(x,y,z) from a thin line
(uniform linear charge density ):
What is ?
A) X B) y'
C) D)
E) Something completely different!!
E =1
4pe0
1
Â2ò ˆ Â ldl'
P=(x,0,0)
x
y
dl'
22 'yx +22' xdl +
Â
r'
r
2.10
Â=Â
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P=(x,0,0)
x
y
dl'
 r'=
(0,y',0)
r
E (
r ) =
l dl'
4pe0Â3ò
Â
2.11
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,so
P=(x,0,0)
x
y
dl'
 r'=
(0,y',0)
r
E (
r ) =
l dl'
4pe0Â3ò
Â
Ex (x,0,0) =l
4pe0
…ò
else Something ))'(
'')
'')
)'(
')
')
2/322
3
2/322
3
Eyx
ydyD
x
ydyC
yx
xdyB
x
xdyA
ò
ò
ò
ò
+
+
2.11
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To find the E- field at P from a thin
ring (radius R, uniform linear charge
density ):
what is ?
E =1
4pe0
1
Â2ò ˆ Â ldl'
Â
P=(0,0,z)
R x
y dl'
B
E) NONE of the arrows shown
correctly represents
Â
A C
D
2.12
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To find the E- field at P from a thin
ring (radius a, uniform linear charge
density ):
what is ?
A)
B) a
C) D) z
E) Something completely different!!
E =1
4pe0
1
Â2ò ˆ Â ldl'
Â
P=(0,0,z)
a x
y dl'
a2 + z2
dl'2
+z2
2.13
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Griffiths p. 63 finds E a distance z from
a line segment with charge density :
What is the approx. form for E, if z>>L?
A) 0 B) 1 C) 1/z D) 1/z^2
E) None of these is remotely correct.
x
(0,0,z)
E =1
4pe0
2lL
z z2 + L2k̂
-L +L
E =2lL
4pe0
× (...)
2.16
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Griffiths p. 63 finds E a distance z from
a line segment with charge density :
What is the approx. form for E, if z<<L?
A) 0 B) 1 C) 1/z D) 1/z^2
E) None of these is remotely correct.
x
(0,0,z)
E =1
4pe0
2lL
z z2 + L2k̂
-L +L
E =2l
4pe0
× (...)
2.16
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D) None of these
To find E at P from a negatively charged sphere
(radius R, uniform volume charge density ) using
what is (given the small
volume element shown)?
E =1
4pe0
1
Â2ò Â̂ r dt '
P=(x,y,z)
x
y
z (x’,y’,z’)
R A
B
C
Â
2.14
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A)
B)
C)
D) E) None of these
E =1
4pe0
1
Â2ò Â̂ r dtP=(X,Y,Z)
X,Y,Z
(X x)2
(Y y)2
(Z z)2
dxdydz
X,Y,Z
(X x)2 (Y y)2 (Z z)2 3/2 dxdydz
X x,Y y,Z z
(X x)2
(Y y)2
(Z z)2
dxdydz
X x,Y y,Z z
(X x)2 (Y y)2 (Z z)2 3/2 dxdydz
1
40(....?)
x
y z (x,y,z)
R
2.15
dq
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A)
B)
C)
D) E) None of these
E =1
4pe0
1
Â2ò Â̂ r dtP=(X,Y,Z)
X,Y,Z
(X x)2
(Y y)2
(Z z)2
dxdydz
X,Y,Z
(X x)2 (Y y)2 (Z z)2 3/2 dxdydz
X x,Y y,Z z
(X x)2
(Y y)2
(Z z)2
dxdydz
X x,Y y,Z z
(X x)2 (Y y)2 (Z z)2 3/2 dxdydz
1
40(....?)
x
y z (x,y,z)
R
2.15
Â