32. Electromagnetic Waves

What is the magnetic field amplitude of an electromagnetic wave that has electric field amplitude

1500 V/m

400

lightbulb emits light uniformly in all directions. What is the electric field amplitude

50 W

10 cm

away from the lightbulb?

260

Alice observes an electric field,

\overset{⇀}{E} = (30 \frac{V}{m}) \hat{k}

, and a magnetic field

\overset{⇀}{B} = (0.10 T) \hat{i}

. Bob is cruising by, with velocity

\overset{⇀}{v} = (100 \frac{m}{s}) \hat{j}

, in Alice's reference frame. What electric field does Bob observe?

331

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T.

You measure the electric field of an electromagnetic wave at a particular moment and find it points in the +z direction. The magnetic field points in the +y direction. In which direction is this wave traveling?

You measure the magnetic field strength of a traveling electromagnetic wave to be $8.0\times10^{-7}T$ , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?

(The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. (c) What is the current in the ring if its resistance is 4.00 Ω?

307

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius r_1 inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b) Find the magnitude of the induced electric field inside the solenoid, at a distance r_1 from its axis. Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric field outside the solenoid, at a distance r_2 from the axis?

434

(II) Our nearest star (other than the Sun) is 4.2 light-years away. That is, it takes 4.2 years for the light it emits to reach Earth. How far away is it in meters?

(II) A light-year is a measure of distance (not time). How many meters does light travel in a year?

Assume that the nearest stars to us have an intrinsic luminosity about the same as the Sun’s. Their apparent brightness, however, is about 10¹¹ times fainter than the Sun. From this, estimate the distance to the nearest stars.

(II) An electromagnetic wave has an electric field given by

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a. What are the wavelength and frequency of the wave?

b. Write down an expression for the magnetic field.

(I) If the electric field in an EM wave has a peak magnitude of 0.45 x 10⁻⁴ V/m, what is the peak magnitude of the magnetic field strength?

Why do some microwave ovens rotate the food container? Suppose the metal walls form a rectangular cavity of dimensions 37 cm x 37 cm x 20 cm. When 2.45-GHz microwaves are continuously introduced into this cavity, reflection of incident waves from the walls sets up standing waves with nodes at the walls. Along the 37-cm dimension of the oven, how many nodes exist (excluding the nodes at the wall) and what is the distance between adjacent nodes? (No heating occurs at these nodes, so rotating the food container gives more even heating of the food.)

Estimate the rms electric field in the sunlight that hits Mars, knowing that the Earth receives about 1350 W/m² and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.

A radio station is allowed to broadcast at an average power not to exceed 25 kW. If an electric field amplitude of 0.020 V/m is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to detect this station.

Suppose that a right-moving EM wave overlaps with a left-moving EM wave so that, in a certain region of space, the total electric field in the y direction and magnetic field in the z direction are given by Eᵧ = E₀ sin(kx - ωt) + E₀ sin(kx + ωt) and Bz = B₀ sin(kx - ωt) - B₀ sin(kx + ωt) (b) Determine the Poynting vector and find the x locations at which it is zero at all times.