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Physics 112 HW
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DC01. The figure at right shows a circular region (radius = 0.05 m) where ⃗𝑬 points out
of the page. In this region at a particular moment of time, the magnitude of ⃗𝑬 is 50
V/m and is increasing out of the page at a rate of 20 V/ms. Use Ampere’s Law to determine the
magnitude and direction of the magnetic field at point P, 0.15 m away from the center of this circular
region.
DC02. A parallel-plate capacitor is being charged
up as shown in the figure. The circular plates
have a radius of 4.00 cm, and at a particular
instant the current to them is 0.280 A. You may
I
assume that the electric field between the plates
is uniform and is given by E = V/d, where d is
the distance between the plates and V is the
voltage across them.
a) What is the displacement current in the
space between the plates?
b) What is the rate at which the electric field between the plates is changing?
c) What is the induced magnetic field between the plates at a distance of 2.00 cm from the axis?
DC03. Again, refer to the figure for DC02 above. Here, the parallel plates have an area of 5.00 cm2 and
are separated by 2.00 mm. The current I has a constant value of 1.80 mA. At time t = 0 the charge on
the plates is zero.
a) Calculate the charge on the plates, the electric field between the plates, and the potential
difference between the plates when t = 0.500 μs.
b) Calculate dE/dt, the time rate of change of the electric field between the plates. Does dE/dt vary
with time?
c) Calculate the displacement current between the plates. How does this compare to the current I?
I
FL07. In the diagram at right, there are two regions with uniform magnetic fields going into and out of
the page (represented by the circled x’s and dots,
Path C
respectively). The magnetic field outside of these circular
Path A
Path B
regions is zero. The left region (solid circle) has a radius of
0.20 m, while the right region (solid circle) has a radius of
0.30 m. The magnitude of the magnetic field through the left
region is increasing out of the page at a rate of 8.5  10-3 T/s,
while that through the right region is increasing into the page
at the same rate. Paths A and B are circular with radius 0.5
⃗ for each path, going in
⃗ ∙ 𝑑𝓵
m. Determine the value of ∮ 𝑬
the direction indicated by the arrows.