Electromagnetic radiation from a $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{mw}$laser is concentrated on a $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{-}{\mathbf{mm}}^{\mathbf{2}}$ area. (a) What is the intensity in$\mathbf{W}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$? (b) Suppose a $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{nC}$nC static charge is in the beam. What is the maximum electric force it experiences? (c) If the static charge moves at$\mathbf{400}\mathbf{m}\mathbf{/}\mathbf{s}$, what maximum magnetic force can it feel?

The power transferred per unit area is the intensity of radiant energy in physics, where the area is measured on a plane perpendicular to the energy's propagation direction.

(a)

Considering the given information,

The power of the EM radiation is $\mathrm{P}=5\times {10}^{-3}\mathrm{W}.$

The area is$\mathrm{A}=1\times {10}^{-6}{\mathrm{m}}^2$

Apply the formula,

The formula for determining the strength of EM radiation is as follows:

$\mathrm{I}=\frac{\mathrm{p}}{\mathrm{A}}$

Putting the values,

$$\begin{gathered} \mathrm{I}=\frac{5\times {10}^{-3}\mathrm{W}}{1\times {10}^{-6}{\mathrm{m}}^2} \\ =5\times {10}^3\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

Therefore, the required intensity of electromagnetic radiation is $5\times {10}^3\mathrm{W}/{\mathrm{m}}^2$

(b)

Considering the given information,

The power of the EM radiation is $\mathrm{P}=5\times {10}^{-3}\mathrm{W}.$

The area is $\mathrm{A}=1\times {10}^{-6}{\mathrm{m}}^2$

Charge$\mathrm{q}=2.0\mathrm{nC}\left(\frac{{10}^{-9}\mathrm{C}}{1\mathrm{nC}}\right)=2.0\times {10}^{-9}\mathrm{C},$

Apply the formula,

The relationship between intensity and the strength of the electric field is provided by,

$\mathrm{I}=\frac{1}{2}{\mathrm{c\epsilon }}_0{\mathrm{E}}_0^2$

The radiation's maximal electric field is:

$$\begin{gathered} {\mathrm{E}}_0=\sqrt{\frac{2\mathrm{I}}{{\mathrm{c\epsilon }}_0}} \\ =\sqrt{\frac{2\times \left(5\times {10}^{-3}\mathrm{W}\right)}{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)\times \left(8.85\times {10}^{-12}{\mathrm{C}}^2/\mathrm{N}-{\mathrm{m}}^2\right)}} \\ =1.94\times {10}^3\mathrm{N}/\mathrm{C} \end{gathered}$$

The electric field's force on the charge is given as:

$\mathrm{F}={\mathrm{qE}}_0$

Putting the values,

$$\begin{gathered} \mathrm{F}=\left(2.0\times {10}^{-9}\mathrm{C}\right)\left(1.94\times {10}^3\mathrm{N}/\mathrm{C}\right) \\ =3.88\times {10}^{-6}\mathrm{N} \end{gathered}$$

Therefore, the required maximum electric force experienced by charge is$3.88\times {10}^{-6}\mathrm{N}$.

(c)

The formula for the magnetic force experienced by a moving charge is:

$\mathrm{F}=\mathrm{q}\left(\mathrm{v}\times \mathrm{B}\right)$

The strength of the magnetic field is:

${\mathrm{B}}_0=\frac{{\mathrm{E}}_0}{\mathrm{C}}$

The moving charge's maximum magnetic force is:

$$\begin{gathered} {\mathrm{F}}_{\max }={\mathrm{qvB}}_0 \\ =\mathrm{qv}\frac{{\mathrm{E}}_0}{\mathrm{C}} \\ =\frac{\left(2\times {10}^{-9}\mathrm{C}\right)\times \left(400\mathrm{m}/\mathrm{s}\right)\left(1.94\times {10}^3\mathrm{N}/\mathrm{C}\right)}{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right)} \\ =5.17\times {10}^{-12}\mathrm{N} \end{gathered}$$

Therefore, the required maximum magnetic force experienced by the charge is$5.17\times {10}^{-12}\mathrm{N}$.