Wings of a morpho butterfly, peacock feathers, lotus leaf surface and sources of parrot fish's bite are some of the natural nano particles.

\(r \propto A^{\frac{1}{3}}  \)
\(\frac{r_{\mathrm{Cu}}}{\mathrm{r}_{\mathrm{Al}}}=\frac{\mathrm{A}_{\mathrm{Cu}}^\frac{1}{3}}{\mathrm{~A}_{\mathrm{Al}}^{\frac{1}{3}}}=\frac{4}{3}  \)
\(\mathrm{r}_{\mathrm{Cu}}=\frac{4}{3} \times 3.6 \mathrm{~F}=4.8 \mathrm{~F}\)

Cathode rays are stream of negatively charged electron.

\(\frac{\mathrm{hc}}{\lambda}  =\phi+\mathrm{K} . \mathrm{E}  .....(1)  \)
\(\frac{2 \mathrm{hc}}{\lambda}  =\phi+3 \mathrm{~K} . \mathrm{E}......(2)\)
multiply eqn. (1) by 3, we get
\(\frac{3 \mathrm{hc}}{\lambda}  =3\phi+3 \mathrm{~K} . \mathrm{E}  .....(3)\)
Subtract eqn. (2) from (3), we get
\(\frac{\mathrm{hc}}{\lambda}  =2\phi \)
\(\phi=\frac{ \mathrm{hc}}{2\lambda}  \)

\(\phi_B =10 t^2-50 t+250  \)
\(e  =\frac{-d \phi_B}{d t}  \)
\(=\frac{-d}{d t}\left(10 t^2-50 t+250\right) \)
=-(20 t - 50) 
=-20 t + 50
When, t = 3 s, e =-20(3) + 50 = -60 + 50
e = -10V

ג = \(\frac{c}{f}=\frac{3 \times10^8}{300 \times 10^6}=1 m\)

\(Φ=\frac { q_{net} }{ { \varepsilon }_{ 0 } } \)
q_net = - q + q + 2q = 2q
Relative permittivity of water = 80
\(\therefore Φ=\frac { q }{{ \varepsilon }_{ r } { \varepsilon }_{ 0 } } \)
\(=\frac{2q}{{ 80 \times \varepsilon }_{ 0 }}=\frac{q}{{ 40 \varepsilon }_{ 0 }}\)

Resistance, \(R=\frac{V}{I}=\frac{4}{2}=2 \ ohm\)