# Determine whether vector field is magnetic or electrostatic

1. Apr 10, 2013

### Roodles01

1. The problem statement, all variables and given/known data
Three vector fields are listed below. Determine whether each of them is electrostatic field or magnetic field.

2. Relevant equations
F1(x, y, z) = A (9yz ex + xz ey + xy ez)
F2(r,∅,z) = A [(cosx/r)er + (sinx/r) e]
F3(r,θ,∅) = Ar2 e(-r/a) er

3. The attempt at a solution
Used matrix to determine the first one
| ex ey ez |
|δ/δx δ/δy δ/δz|
|yz xz xy |
as electrostatic (curl = 0 = -δB/δt) & fine with the how & what defines an electrostatic field
but . . . .
not sure how to determine whether one of these fields is magnetic or not!

Thank you.

2. Apr 10, 2013

### ehild

What do you know about the divergence of the electric and magnetic fields?

ehild

3. Apr 10, 2013

### Roodles01

1. divergence should be proportional to the density of magnetic "charge" (div B = 0 - no monople law)

2. div E = ρ / E0
(and for a conservative (electrostatic) field the curl should be zero. (Faradays law - curl E - -∂B/∂t))

The difference is that I "get" 2 and can show this by the matrix I showed above, but not sure how to apply 1 to come to the conclusion of whether it's an electrostatic field or magnetic field.

Can I go down a similar route to find that divB = 0

Last edited: Apr 10, 2013
4. Apr 10, 2013

### Roodles01

OK, OK I've kicked off a bit early.
I will be using the equations booklet & make sure I look at it to complete problems in the way I've been taught (although coming back to it from a while ago dulls the mind if you're not using it).

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