Determine whether vector field is magnetic or electrostatic

[Roodles01]

Homework Statement

Three vector fields are listed below. Determine whether each of them is electrostatic field or magnetic field.

Homework Equations

F1(x, y, z) = A (9yz e_x + xz e_y + xy e_z)
F2(r,∅,z) = A [(cosx/r)er + (sinx/r) e_∅]
F3(r,θ,∅) = Ar² e^(-r/a) e_r

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!

Help please.
Thank you.

 

[ehild]

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

ehild

 

[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

 

[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).

 

[paranormal]

To determine whether a vector field is magnetic or electrostatic, we can use the following criteria:

1. Magnetic fields are created by moving charges, while electrostatic fields are created by stationary charges. Therefore, if the vector field is created by moving charges, it is likely a magnetic field.

2. Magnetic fields have a non-zero curl, while electrostatic fields have a curl of zero. The curl can be calculated using the formula: curl(F) = (∂Fz/∂y - ∂Fy/∂z)ex + (∂Fx/∂z - ∂Fz/∂x)ey + (∂Fy/∂x - ∂Fx/∂y)ez. If the curl is non-zero, it is likely a magnetic field.

3. Magnetic fields have a non-zero divergence, while electrostatic fields have a divergence of zero. The divergence can be calculated using the formula: div(F) = (∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z). If the divergence is non-zero, it is likely a magnetic field.

Applying these criteria to the given vector fields, we can determine the following:

1. F1(x, y, z) = A (9yz ex + xz ey + xy ez) is likely an electrostatic field, as it is created by stationary charges.

2. F2(r,∅,z) = A [(cosx/r)er + (sinx/r) e∅] is likely a magnetic field, as it has a non-zero curl (∂Fz/∂r ≠ 0).

3. F3(r,θ,∅) = Ar2 e(-r/a) er is likely a magnetic field, as it has a non-zero curl (∂Fz/∂θ ≠ 0) and non-zero divergence (∂Fr/∂r ≠ 0).

It is important to note that without more context or information about the vector fields, it is difficult to definitively determine whether they are magnetic or electrostatic. However, using these criteria can give us a good indication.