Chapter 22, Problem 26P

To determine

The radiation pressure and force exerted on the fingertip placed at that point.

Answer to Problem 26P

The radiation pressure is $\text{4}{\text{.14×10}}^{\text{-6}}{\text{N/m}}^{\text{2}}$ and force is $\text{4}{\text{.1× 10}}^{\text{-10}}\text{N}$ .

Explanation of Solution

Given info:

Power of the bulb, $\text{P=100}\text{W}$

Distance of the figure from the bulb, $\text{r}\text{= 8}\text{.0}\text{cm}$

Formula used:

Radiation pressure:

  ${\text{P}}_{\text{rad}}\text{=}\frac{\overline{\text{I}}}{\text{cA}}$

Where, $\text{I}$ is the energy per unit area per unit time, c is the speed of light $\text{c}$ = ${\text{3×10}}^{\text{8}}\text{m/s}$ and A is area.

Force:

  ${\text{F = P}}_{\text{rad}}\text{A}$

Where, ${\text{P}}_{\text{rad}}$ is the pressure and A is area.

Calculation:

Substituting the given values in the formula, ${\text{P}}_{\text{rad}}\text{=}\frac{\overline{\text{I}}}{\text{cA}}$

  $\text{=}\frac{\text{100}\text{W}}{\text{4π}{\left({\text{8×10}}^{\text{-2}}\right)}^{\text{2}}\left(\text{3}{\text{.00 × 10}}^{\text{8}}\text{m/s }\right)}\text{=4}{\text{.14×10}}^{\text{-6}}{\text{N/m}}^{\text{2}}$

For the force exerted is calculated by the pressure and area of $\text{fingertip to be 1}\text{.0}{\text{cm}}^{\text{2}}$ approximately,

  ${\text{F = P}}_{\text{rad}}\text{A}$

  $\text{=(4}{\text{.1×10}}^{\text{-6}}{\text{N/m}}^{\text{2}}\text{) (1}{\text{.0 × 10}}^{\text{-4}}\text{)}$

  $\text{= 4}{\text{.1× 10}}^{\text{-10}}\text{N}\text{.}$

Conclusion:

The radiation pressure is $\text{4}{\text{.14×10}}^{\text{-6}}{\text{N/m}}^{\text{2}}$ and force exerted on figure is $\text{4}{\text{.1× 10}}^{\text{-10}}\text{N}$ .