An infinitely large plate has uniform surface charge density +o where o is a positive number. The plate moves with speed v along the x-direction. Since the charges are moving with the plate, they form a uniform two dimensional surface current density K whose value is |K| : by a line of length L is I = |K|L. See Fig. 2(A) below. = ov. Namely, the electric current I passing
An infinitely large plate has uniform surface charge density +o where o is a positive number. The plate moves with speed v along the x-direction. Since the charges are moving with the plate, they form a uniform two dimensional surface current density K whose value is |K| : by a line of length L is I = |K|L. See Fig. 2(A) below. = ov. Namely, the electric current I passing
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Transcribed Image Text:An infinitely large plate has uniform surface charge density +o where o is a positive number. The plate
moves with speed v along the x-direction. Since the charges are moving with the plate, they form a uniform
two dimensional surface current density K whose value is |K|
by a line of length L is I = |K|L. See Fig. 2(A) below.
= ov. Namely, the electric current I passing
(A)
K
X
(B)
(C)
+o
V
V
Ampere loop
FIGURE 2
(a) By symmetry, the value of magnetic field B due to the current K above or below the plate is the
same, and B is obviously parallel to the plate. In which direction is B pointing above the plate?
Below the plate?
(b) Find the value of the magnetic field B above or below the plate by Ampere's law, using the rectan-
gular Ampere loop shown in the Fig. 2(B). Again, by symmetry, the values of B must be the same
above or below the plate, and it must be a constant that only depends on |K| and v.
Hint: Compute S B · dl´along the four segments of the Ampere loop and pay attention if B || dl´or
BIdl on each of the four segments.
(c) Now, suppose you have two parallel infinitely large plates, but one with +o charge density and the
other with -o charge density, see Fig. 2(C). Both move with speed v along the x-direction. What
is the magnetic field in between the two plates?
(d) A positive point charge q enters in between the plates and moves in the +x-direction with speed vg.
Determine the force on q due to the magnetic field.
(e) Now, the two plates stop moving (v = 0), but for some strange reason the value of charge density
on both plates reduces with time t: o = 0,e-at where a and o, are positive constants. Calculate
the displacement current density in the space between the two plates.
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