Field of uniformly moving charge
Field of uniformly moving charge
LL2 Section 38
Origins are the same at t = 0.
Coordinates of the charge e
K: (Vt, 0, 0)
K’: (0, 0, 0)
4-potential in K’, the rest frame of
e
.
A
i
= (
’,
A
’)
= Distance from charge to field point according to an observer in K’
Scalar potential of moving charge in lab frame K
We need to express
in
terms of K-system (lab)
coordinates.
Vector potential of moving charge in lab frame K
In K’ frame, there is only the static electric field of a point charge.
Position of the field with respect to the
charge according to an observer in K’.
Electric fields of moving charge as measured in the lab
=
(24.2)
Substitute transformations
for x’, y’, z’, and R’ (HW)
R
is distance
from moving e
to fixed P
according to K
R
is distance from moving e to fixed P according to K
Lab coordinates and angle of fixed field point relative to the moving charge
=
Position of field point with
respect to charge
according to observer in K
Angle according to observer in K
Field point
Electric field in lab from moving charge
Smallest value at
= 0 and
i.e. parallel to the direction of motion
Largest value at
=
/2
i.e. perpendicular to
V
For V c, the electric field is compressed
to a narrow range about
=
/2 with
HW
H
-field in K system found by (24.5):
H
= (1/c)
V x E
(H’= 0 in K’)
For V << c, electric field is not deformed
But we still get a magnetic field due to the current of the moving charge
This content explores the electric fields and potentials of moving charges in different frames of reference, discussing transformations and observations in the lab and K frames. It covers aspects like scalar and vector potentials, field positioning, and field point measurements.
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Presentation Transcript
Field of uniformly moving charge LL2 Section 38
Origins are the same at t = 0. Coordinates of the charge e K: (Vt, 0, 0) K : (0, 0, 0)
4-potential in K, the rest frame of e. Ai = ( , A ) = Distance from charge to field point according to an observer in K
Scalar potential of moving charge in lab frame K We need to express in terms of K-system (lab) coordinates. =
In K frame, there is only the static electric field of a point charge. Position of the field with respect to the charge according to an observer in K .
Electric fields of moving charge as measured in the lab (24.2) = Substitute transformations for x , y , z , and R (HW) R is distance from moving e to fixed P according to K
Lab coordinates and angle of fixed field point relative to the moving charge Field point Position of field point with respect to charge according to observer in K Angle according to observer in K =
Electric field in lab from moving charge Smallest value at = 0 and i.e. parallel to the direction of motion Largest value at = /2 i.e. perpendicular to V
For V c, the electric field is compressed to a narrow range about = /2 with HW https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTzWBcluEumyzMcPNbM9J03XkMn5vL1sPW8mCQWNgaCySysTpXK
H-field in K system found by (24.5): H = (1/c) V x E (H = 0 in K ) For V << c, electric field is not deformed But we still get a magnetic field due to the current of the moving charge
