30: Problem 30.45

INTRO:
The starter motor of a car engine draws a current of 180 A from the battery. The copper wire to the motor is 4.30 mm in diameter and 1.2 m long. The starter motor runs for 0.630 s until the car engine starts.
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PART A:
How much charge passes through the starter motor?
Express your answer with the appropriate units.

SOLUTION:

Givens/ Conversions:

I = 180 A
L = 1.2 m
d = 4.30 mm = 4.3×10^-3 m
t = 0.630 s

Using eq. (30.10): Q = I⋅Δt...

Q = (180 A)(0.630 s)
⇒ Q = 113.4 C (A⋅s = C)

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PART B:
How far does an electron travel along the wire while the starter motor is on?
Express your answer with the appropriate units.

SOLUTION:
Using eq. (30.13) ... J = I/A = n_e⋅e⋅v_d
rearranging... v_d = I/(A⋅n_e⋅e)

this equation has all knowns and solves for the speed. first step for determining distance traveled over time, right? right.
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using table (30.1) ... n_ecopper = 8.5×10²⁸ m^-3

We know that the distance traveled = velocity⋅time
∴ distance = I⋅Δt/(A⋅n_e⋅e)

= (180 A)(0.63 s)/[(π/4⋅(4.3×10^-3 m)²)(8.5×10²⁸ m^-3)(1.602×10^-19C)]
= 5.735×10^-4 m
⇒ 0.574 mm

34: Traveling Electromagnetic Wave

INTRO:
Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other.
The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by

E =E₀sin(kx−ωt)j^
B =B₀sin(kx−ωt)k^

This wave is linearly polarized in the y direction.

Part A:
In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E₀ and B₀ are the __________ of the electric and magnetic fields.
Choose the best answer to fill in the blank.

A) maxima
B) amplitudes
C) wavelengths
D) velocities

Part B:
The variable ω is called the __________ of the wave.
Choose the best answer to fill in the blank.

A) velocity
B) angular frequency
C) wavelength

Part C:
The variable k is called the __________ of the wave.
Choose the best answer to fill in the blank.

A) wavenumber 
B) wavelength
C) velocity
D) frequency

Part D:
What is the mathematical expression for the electric field at the point x=0, y=0, z at time t?

A) E = E₀sin(−ωt)j^
B) E = E₀sin(−ωt)k^
C) E = 0
D) E = E₀sin(kz−ωt)i^
E) E = E₀sin(kz−ωt)j^

Part E:
For a given wave, what are the physical variables to which the wave responds?

A) x only
B) t only
C) k only
D) ω only
E) x and t
F) x and k
G) ω and t
H) k and ω

Part F:
What is the wavelength λ of the wave described in the problem introduction?
Express the wavelength in terms of the other given variables and constants like π.

SOLUTION:
λ = 2π⋅1/k

Part G:
What is the period T of the wave described in the problem introduction?
Express the period of this wave in terms of ω and any constants

SOLUTION:
frequency = 1/period ↔ period = 1/frequency
f = 1/T ↔ T = 1/f
f = ω/[2π] → T = 2π⋅1/ω

Part H:
What is the velocity v of the wave described in the problem introduction?
Express the velocity in terms of quantities given in the introduction (such as ω and k) and any useful constants.

SOLUTION:
v = fλ & λ = 2π⋅1/k & f = ω/[2π] 
so... v = 2π⋅1/k⋅ω/[2π] = ω/k