holtvg
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What are the differences between these three types of fields or are they all interrelated and the same.
Electric, magnetic, and electromagnetic fields
- Context: Undergrad
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rbj
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just to add, explicitly, that the classical magnetic interaction can be understood as a manifestation of only the electrostatic interaction but with the effects of (special) relativity taken into consideration. i.e. the magnetic field and resulting force on charged particles is essentially nothing new or different than the electric field. but, in classical physics (where there is no SR concepts such as time dilation, etc.), the magnetic field has to be described or modeled as a different or separate action than the electrostatic field.
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Welcome to PF!
Hi holtvg! Welcome to PF!
Electric field: a 3-vector: (Ex, Ey, Ez)
Magnetic field: a 3-vector: (Bx, By, Bz)
Electromagnetic field: a 2-form (with 6 components): (Ex, Ey, Ez;Bx, By, Bz)
They are interrelated in the same way that the x and y components of a vector are interrelated … if you rotate the x and y axes, the x and y components of the same vector get mixed together a little.
Similarly, observers with different velocities see the E and B fields mixed together … for example, a stationary electron has an E field and a zero B field, but a moving electron has slightly different E field, and a small B field also.
(this is not a relativity thing … Maxwell knew all about it!)
holtvg said:
Hi holtvg! Welcome to PF!
Electric field: a 3-vector: (Ex, Ey, Ez)
Magnetic field: a 3-vector: (Bx, By, Bz)
Electromagnetic field: a 2-form (with 6 components): (Ex, Ey, Ez;Bx, By, Bz)
They are interrelated in the same way that the x and y components of a vector are interrelated … if you rotate the x and y axes, the x and y components of the same vector get mixed together a little.
Similarly, observers with different velocities see the E and B fields mixed together … for example, a stationary electron has an E field and a zero B field, but a moving electron has slightly different E field, and a small B field also.
(this is not a relativity thing … Maxwell knew all about it!)
granpa
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tiny-tim said:
a tensor?
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granpa said:
Hi granpa!
Yes, any 2-form can be represented by an antisymmetric second-order tensor.
But a 2-form is easier because:
i] it has only 6 components, while the tensor has 16 components, 4 of which are 0, and 6 of the remaining 12 are minus the other 6;
ii] it makes many equations much more obvious (in partiuclar, Lorentz force and Maxwell's equations).
granpa
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sort of like a pseudovector. a shorthand way of writing a tensor.
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Hi granpa!
Yes, a pseudovector in 3-space (like angular momentum, or any other cross-product of two 3-vectors) is a 2-form , and can be represented as an anti-symmetric tensor.
(though a pseudovector in 4-space is a 3-form, like current
)
granpa said:
Yes, a pseudovector in 3-space (like angular momentum, or any other cross-product of two 3-vectors) is a 2-form , and can be represented as an anti-symmetric tensor.
(though a pseudovector in 4-space is a 3-form, like current
)