Question

Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 1.00×1011V/m for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on a 1.00-mm2 area?

Answer 1

Explanation:

It is given that,

Maximum electric field, $E=10^{11}\ V/m$

Time taken, $t=1\ ns=10^{-9}\ s$

(a) Maximum magnetic field, $B=\dfrac{E}{c}$

$B=\dfrac{10^{11}\ V/m}{3\times 10^8\ m/s}$

B = 333.33 T

(b) Intensity of beam, $I=\dfrac{E^2}{2\mu_o c}$

$I=\dfrac{(10^{11})^2}{2\times 4\pi \times 10^{-7}\times 3\times 10^8}$

$I=1.32\times 10^{19}\ W/m^2$

(c) Energy delivered by the pulse, $E=I\times A\times t$

$E=1.32\times 10^{19}\times 10^{-6}\times 10^{-9}$

E = 13200 J

Hence, this is the required solution.