For the passing reference frames in Fig. 37-25, events A and B occur at the following spacetime coordinates: according to the unprimed frame, (x A , t A ) and (x B , t B ); according to the primed frame, (x' A , t' A ) and (x' B , t' B ). In the unprimed frame, ∆t = t B − t A = 1.0 µs and Δx = x B − x A = 400 m. (a) Find an expression for ∆x' in terms of the speed parameter ß and the given data. Graph ∆x' versus ß for two ranges of ß: (b) 0 to 0.01 and (c) 0.1 to 1. (d) At what value of ß is ∆x' minimum, and (e) what is that minimum?
For the passing reference frames in Fig. 37-25, events A and B occur at the following spacetime coordinates: according to the unprimed frame, (x A , t A ) and (x B , t B ); according to the primed frame, (x' A , t' A ) and (x' B , t' B ). In the unprimed frame, ∆t = t B − t A = 1.0 µs and Δx = x B − x A = 400 m. (a) Find an expression for ∆x' in terms of the speed parameter ß and the given data. Graph ∆x' versus ß for two ranges of ß: (b) 0 to 0.01 and (c) 0.1 to 1. (d) At what value of ß is ∆x' minimum, and (e) what is that minimum?
For the passing reference frames in Fig. 37-25, events A and B occur at the following spacetime coordinates: according to the unprimed frame, (xA, tA) and (xB, tB); according to the primed frame, (x'A, t'A) and (x'B, t'B). In the unprimed frame, ∆t = tB− tA = 1.0 µs and Δx = xB− xA = 400 m. (a) Find an expression for ∆x' in terms of the speed parameter ß and the given data. Graph ∆x' versus ß for two ranges of ß: (b) 0 to 0.01 and (c) 0.1 to 1. (d) At what value of ß is ∆x' minimum, and (e) what is that minimum?
1. A charge of -25 μC is distributed uniformly throughout a spherical volume of radius 11.5 cm.
Determine the electric field due to this charge at a distance of (a) 2 cm, (b) 4.6 cm, and (c) 25 cm from
the center of the sphere.
(a) =
=
(b) E =
(c)Ẻ =
=
NC NC NC
1.
A long silver rod of radius 3.5 cm has a charge of -3.9
ис
on its surface. Here ŕ is a unit vector
ст
directed perpendicularly away from the axis of the rod as shown in the figure.
(a) Find the electric field at a point 5 cm from the center of the rod (an outside point).
E =
N
C
(b) Find the electric field at a point 1.8 cm from the center of the rod (an inside point)
E=0
Think & Prepare
N
C
1. Is there a symmetry in the charge distribution? What kind of symmetry?
2. The problem gives the charge per unit length 1. How do you figure out the surface charge density σ
from a?
1. Determine the electric flux through each surface whose cross-section is shown below.
55
S₂
-29
S5
SA
S3
+ 9
Enter your answer in terms of q and ε
Φ
(a) s₁
(b) s₂
=
-29
(C) Φ
զ
Ερ
(d) SA
=
(e) $5
(f) Sa
$6
=
II
✓
-29
S6
+39
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