Two moving charged particles exert forces on each other because each one creates a magnetic field in which the other moves (see Problem 4.6). These two forces are proportional to v 1 × v 2 × r and v 2 × v 1 × ( − r ) where r is the vector joining the particles. By using ( 3.9), show that these forces are equal and opposite (Newton’s third "law") if and only if r × v 1 × v 2 = 0. Compare Problem 14.
Two moving charged particles exert forces on each other because each one creates a magnetic field in which the other moves (see Problem 4.6). These two forces are proportional to v 1 × v 2 × r and v 2 × v 1 × ( − r ) where r is the vector joining the particles. By using ( 3.9), show that these forces are equal and opposite (Newton’s third "law") if and only if r × v 1 × v 2 = 0. Compare Problem 14.
Two moving charged particles exert forces on each other because each one creates a magnetic field in which the other moves (see Problem 4.6). These two forces are proportional to
v
1
×
v
2
×
r
and
v
2
×
v
1
×
(
−
r
)
where
r
is the vector joining the particles. By using ( 3.9), show that these forces are equal and opposite (Newton’s third "law") if and only if
r
×
v
1
×
v
2
=
0.
Compare Problem 14.
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.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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