[ T ] The fence vector F acting on a proton with an electric charge of 1 .6×10 -19 C moving in a magnetic ?eld B where the velocity vector v is given by F = 1.6 × 10 − 19 ( v × B ) (here, v is expressed in meters per second, B in T , and F in N ). If the magnitude of force F acting on a proton is 5.9 × 10 − 17 N and the proton is moving at the speed of 300 m/sec in magnetic ?eld B of magnitude 2.4 T , find the angle between velocity vector v of the proton and magnetic ?eld B . Express the answer in degrees rounded to the nearest integer.
[ T ] The fence vector F acting on a proton with an electric charge of 1 .6×10 -19 C moving in a magnetic ?eld B where the velocity vector v is given by F = 1.6 × 10 − 19 ( v × B ) (here, v is expressed in meters per second, B in T , and F in N ). If the magnitude of force F acting on a proton is 5.9 × 10 − 17 N and the proton is moving at the speed of 300 m/sec in magnetic ?eld B of magnitude 2.4 T , find the angle between velocity vector v of the proton and magnetic ?eld B . Express the answer in degrees rounded to the nearest integer.
[
T
]
The fence vector
F
acting on a proton with an electric charge of
1
.6×10
-19
C
moving in a magnetic ?eld
B
where the velocity vector
v
is given by
F
=
1.6
×
10
−
19
(
v
×
B
)
(here,
v
is expressed in meters per second,
B
in
T
,
and
F
in
N
). If the magnitude of force
F
acting on a proton is
5.9
×
10
−
17
N
and the proton is moving at the speed of
300
m/sec
in magnetic ?eld
B
of magnitude
2.4
T
, find the angle between velocity vector
v
of the proton and magnetic ?eld
B
. Express the answer in degrees rounded to the nearest integer.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
3m
A. Find the unit vector that makes an angle (0 = - with the positive x-axis.
A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration.
HINT
(a)
the magnitude (in N) of the magnetic force acting on the ion
N
(b)
the magnitude (in m/s2) of the ion's acceleration
m/s2
An object is spinning at a constant speed on the end of a string, according to the position vector r(t) = a cos ωti + a sin ωtj. (a) When the angular speed ω is doubled, how is the centripetal component of acceleration changed? (b) When the angular speed is unchanged but the length of the string is halved, how is the centripetal component of acceleration changed?
Finite Mathematics & Its Applications (12th Edition)
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