Question

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Answer 1

Waves carry energy, so power transmitted along a string depends on amplitude and frequency and the nature of the medium \[P_{av} = \frac{ 1 }{ 2 }\sqrt{\mu F} \omega^2A^2\] average power for sinusoidal wave on a string mhm.
Classically energy of EM wave depends only on amplitude of the electric field, and not the frequency of the light. \[I = S_{av} = \frac{ E_{\max}B_{\max} }{ 2 \mu_0 } = \frac{ E_\max^2 }{ 2 \mu_0c } = \frac{ 1 }{ 2 }\sqrt{\frac{ \epsilon_0 }{ \mu _0 }}E_\max^2=\frac{ 1 }{ 2 }\epsilon_0c E_\max^2\] intensity of a sinusoidal wave in a vacuum

Answer 2

E&M then
\[F_e = k \frac{ q_1q_2 }{ r^2 }~~ and ~~ U_e = k \frac{ q_1q_2 }{ r }\] Coulomb's law
\[F_e = - \frac{ \partial U_e }{ \partial r }\] \[F_{EM} = q (E+v \times B)\]
Electric field (E) and magnetic field (B), electric potential energy (U) and electrical potential (V) \[F_e = qE ~~ and~~U_e = qV\]

Answer 3

Deocritus and Leucippus (460-370 BC) reasoned matter must have a component very small that was indivisible, how.
1897 J.J. Thompson measures e/m of cathode rays (electrons)
1909 Millikan "measures" the charge, e, on electron, *cough* stole credit from his students *cough* cathode ray tube

Answer 4

Photoelectric effect, ejection of electron from metals, mhm yes pretty simple concept, definitely amazing discovery, yay Einstein! conservation of energy \[E_{light}=1/2m_ev^2+ \phi \] \[\phi = work~function\] meaning the minimum energy required for an electron to escape from the surface.

What was observed during the experiment:
(i) Electrons emitted immediately, regardless of intensity of light
(ii) Increasing intensity of light increased the current which is the number of electrons, but not the maximum KE
(iii) Stopping potential depends on frequency of the light
\[K_{\max}=\frac{ 1 }{ 2 }m_ev^2_{\max}=eV_s\] leading Eistein to postulate light shining on metal cathode is made up of photons of energy hf.
\[E_{photon}=hf=\frac{ hc }{ \lambda } \] hence \[hf = eV_s + \phi\]