Question

The light from a red laser pointer has a wavelength of about 600 nm. If this laser has a power of 0.18 mW, what is the momentum carried by a 1.8-s pulse of this radiation? (in kg · m/s)

The magnetic field associated with an electromagnetic wave has
an amplitude of 1.6 *μ*T.

(a) What is the amplitude of the electric field associated with this wave? (in V/m)

(b) What is the intensity of this wave? (W/m^{2)}

(c) What is the radiation pressure associated with this wave?
(N/m^{2)}

(d) How much momentum is carried by a 1.3-s pulse of this wave
over an area of 16 m^{2}? (kg · m/s)

Answer #1

We know that, E = p c

where, c = speed of light = 3 x 10^{8} m/s

(0.18 x 10^{-3} J/s) (1.8 s) = p (3 x 10^{8}
m/s)

p = (0.324 x 10^{-3} J) / (3 x 10^{8} m/s)

p = 0.108 x 10^{-11} kg.m/s

**p = 1.08 x 10 ^{-12} kg.m/s**

(a) What is the amplitude of the electric field associated with this wave?

using a formula, we have

E_{0} = c B_{0} (3 x
10^{8} m/s) (1.6 x 10^{-6} T)

E_{0} = 4.8 x 10^{2} V/m

**E _{0} = 480 V/m**

(b) What is the intensity of this wave?

using a formula, we have

I = (c _{0}
E^{2}) / 2

I = [(3 x 10^{8} m/s) (8.85 x 10^{-12}
C^{2}/Nm^{2}) (480 V/m)^{2}] / 2

**I = 305.8 W/m ^{2}**

(c) What is the radiation pressure associated with this wave?

using a formula, we have

*P*_{rad} = I / c = (305.8 W/m^{2}) / (3
x 10^{8} m/s)

*P*_{rad} = 101.9 x 10^{-8}
N/m^{2}

*P*_{rad} = 1.02 x 10^{-6}
N/m^{2}

(d) How much momentum is carried by a 1.3-s pulse of this wave
over an area of 16 m^{2}?

using a formula, we have

p =
*P*_{rad} A t = (1.02 x 10^{-6}
N/m^{2}) (16 m^{2}) (1.3 sec)

**p = 2.12 x
10 ^{-5} kg.m/s**

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