-----Problem below-----
Using the Lorenz gauge calculate the scalar and vector
potentials generated by a point charge moving along trajectory r_0
(t) and find electric and magnetic field generated by this
particle.
Show that the following two vector fields are conservative and
find associated scalar potentials.
(a) F = 2ρsin(2φ) ρ + 2ρcos(2φ) φ
+ k
(b) F = (2r cos2 φ + sinθ cosφ) r + cosθ cosφ
θ − [r(sin(2φ)/sinθ) + sinφ]
φ
a) show that the vector field F= <siny, xcosy, -sinz> is
conservative by finding a scalar f such that ∇f=F.
b) use this fact to ecaluate ∫C F•dr along the given curve C
where C is the line segment from (0,0,0) to (4, π/2, π/2).
Identify each of the
following quantities as a vector or a scalar quantity. Select the
appropriate term from the dropdown beside each sentence.
700 J of kinetic
energy.
Answer 1Choose...VectorScalar
A distance of 38
m.
Answer 2Choose...VectorScalar
A distance of 60 miles
due north.
Answer 3Choose...VectorScalar
A temperature of 452
oC.
Answer 4Choose...VectorScalar
An acceleration of 80
m s-2 towards the east.
Answer 5Choose...VectorScalar
A tensile force of 600
N.
Answer 6Choose...VectorScalar
A speed of 50 m
s-1 at a...
Essay
The ‘valentine
vector’ says,
“I was only
a scalar
until you
came along
and gave me
direction.”
What is your
scientific insight
in this statement?
1.Find the derivative of the product between a scalar function
and a vector function using the product formula.
2. Find the volume of an irregular solid using triple
integration, the first integral should have at least one limit with
variables.
3. Determine the moment of inertia of an irregular solid using
triple integration. the first integral should have at least one
limit with variables.
4. Find the angle between two lines using dot product. the two
lines should not pass...