Question 13
A region contaings an electric field
E
= 7.4
i
ˆ
+ 2.8
j
ˆ
kN / C and a magnetic field
B
=15
j
ˆ
+36
k
ˆ
mT. Find the electromagnetic force on (a) a stationary proton, (b) an electron
moving with velocity
v
= 6.1
i
ˆ
Mm / s.
(a) We’ll use the Lorentz force law,
F
=q(
E
+
v
×
B
). For part (a),
v
= 0.
N
F
or
N
j
i
F
N
j
i
F
E
q
F
15
16
16
3
19
10
27
.
1
ˆ
10
49
.
4
ˆ
10
9
.
11
10
)
ˆ
8
.
2
ˆ
4
.
7
(
10
602
.
1
!
!
!
!
"
=
"
+
"
=
"
+
#
"
=
=
v
v
v
v
(b) Next we use the same equation with the given velocity. Since we’re doing an electron
this time, we’ll use negative e.
(
)
(
)
(
)
(
)
(
)
(
)
N
F
or
N
k
j
i
F
N
j
k
j
i
F
N
k
j
i
j
i
F
B
v
E
q
F
15
16
3
19
3
6
3
19
10
7
.
37
10
ˆ
6
.
146
ˆ
3
.
347
ˆ
9
.
11
10
ˆ
6
.
219
ˆ
5
.
91
ˆ
8
.
2
ˆ
4
.
7
10
602
.
1
10
ˆ
36
ˆ
15
ˆ
10
1
.
6
10
ˆ
8
.
2
ˆ
4
.
7
10
602
.
1
!
!
!
!
!
"
=
"
!
+
!
=
"
!
+
+
"
!
=
"
+
"
"
+
"
+
"
!
=
"
+
=
v
v
v
v
v
v
v
Question 22
Show that the orbital radius of a charged particle moving at right angles to a magnetic
field B can be written
qB
Km
r
2
=
where K is the kinetic energy in joules, m the particle mass, and q its charge.
To solve this problem you can either use equation 293 and relate v to K (K=
½
mv
2
), or
you can derive the equation from first principles. In 2A you learned that if an object
moves in a circle, it must be experiencing a force F=mv
2
/r to keep it moving in that
circle. Then we observe that for a particle moving perpendicular to the B field, F=qvB.
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 Spring '08
 WORMER
 Physics, Force, Magnetic Field, #, qV

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