Co-ordinate Systems

Question 1

Using the “Gangsta” sign gesture for the cross product (AXB), what does the pointer and middle finger & thumb represent?

Answer 1

Thumb: A
Pointer Finger: B
Middle Finger: AXB

Question 2

What does |AXB| equal?

Answer 2

Magnitude of AXB = ABsinα

Question 3

If C=AXB, what is C•A and C•B?

Answer 3

0 as they are orthogonal

Question 4

What is dSx for a Cartesian System?

Answer 4

[xhat]dydz

Question 5

What is dSy for a Cartesian System?

Answer 5

[yhat]dxdz

Question 6

What is dSz for a Cartesian System?

Answer 6

[zhat]dxdy

Question 7

What is dV for a Cartesian System?

Answer 7

dxdydz

Question 8

What is the gradient of F equal to?

Answer 8

SEE: [img]http://mathworld.wolfram.com/images/equations/Divergence/NumberedEquation4.gif[/img]

Question 9

What is Divergence?

Answer 9

Divergence is Flux/Volume i.e. Flux per unit Volume

Question 10

When is flux positive?

Answer 10

When leaving a surface

Question 11

When is flux negative?

Answer 11

When entering a surface

Question 12

What is flux?

Answer 12

Flux is the net amount of something passing through a surface

Question 13

What is it called when the divergence of A is greater than 0?

Answer 13

A source

Question 14

What is it called when the divergence of A is less than 0?

Answer 14

A sink

Question 15

What do we call ϕ?

Answer 15

Azimuth

Question 16

Vector representation of A in Cylindrical Co-Ord system?

Answer 16

A= Ar[rhat] + Aϕ[ϕhat] + Az[zhat]

Question 17

What is the length differential in a Cylindrical system?

Answer 17

dl= [rhat]dr + [ϕhat]rdϕ + [zhat]dz

Question 18

What is the differential length of an arc formed in the azimuth plane for Cylindrical Co-Ords?

Answer 18

rdϕ

Question 19

What is the volume differential dV for a Cylindrical system?

Answer 19

dV = rdϕdrdz (All the lengths multiplied)

Question 20

What is dSr for a Cylindrical system?

Answer 20

[rhat]rdϕdz

Question 21

What is dSϕ for a Cylindrical system?

Answer 21

[ϕhat]drdz

Question 22

What is dSz for a Cylindrical system?

Answer 22

[zhat]rdϕdr

Question 23

What is the name of Θ?

Answer 23

Zenith angle

Question 24

What is the value of elevation?

Answer 24

90-Θ

Question 25

What is the principal plane for r in Spherical Co-Ords?

Answer 25

A Circle

Question 26

What is the principal plane for Θ in Spherical Co-Ords?

Answer 26

A Cone

Question 27

What is the principal plane for ϕ in Spherical Co-Ords?

Answer 27

A plane

Question 28

What is the length differential for in Spherical Co-Ords?

Answer 28

dl = [rhat]dr + [Θhat]rdΘ + [ϕhat]rsinΘdϕ

Question 29

What is the formula for a differential arc formed on the ϕ plane in Spherical Co-Ords? (Hint: dependant on r and Θ)

Answer 29

rsinΘdϕ

Question 30

What is dSr in Spherical Co-ords?

Answer 30

[rhat]r^2sinΘdϕdΘ

Question 31

What is dSΘ in Spherical Co-ords?

Answer 31

[Θhat]rsinΘdϕdr

Question 32

What is dSϕ in Spherical Co-ords?

Answer 32

[ϕhat]rdΘdr

Question 33

What is dV in Spherical Co-ords?

Answer 33

r^2sinΘdΘdrdϕ