Category: HC Verma Part 2: Modern Physics

Problem Statement Determine the electric field for the configuration described: In an electromagnetic wave travelling through free space, the electric field amplitude is $E_0 = 120$ V/m. Calculate the intensity of the wave. $I = \frac{E_0^2}{2\mu_0 c}$; impedance of free space $Z_0 = \mu_0 c = 377\;\Omega$ Step 1: $$I = \frac{E_0^2}{2\mu_0 c} = \frac{(120)^2}{2\times377}…

Problem Statement Solve the oscillation/wave problem: X-rays have frequencies ranging from $3\times10^{16}$ Hz to $3\times10^{19}$ Hz. Find the corresponding range of wavelengths. $\lambda = c/f$ Step 1: For $f_{min} = 3\times10^{16}$ Hz (longest wavelength): $$\lambda_{max} = \frac{3\times10^8}{3\times10^{16}} = 10^{-8}\text{ m} = 10\text{ nm}$$ Step Given Information $\lambda_{max} = \frac{3\times10^8}{3\times10^{16}} = 10^{-8}\text{ m} = 10\text{ nm}$…

Problem Statement Solve the capacitor/capacitance problem: A parallel-plate capacitor with plate area $A = 0.02$ m² has an electric field between the plates increasing at $dE/dt = 10^{12}$ V/(m·s). Find the displacement current flowing between the plates. Displacement current: $I_d = \varepsilon_0\frac{d\Phi_E}{dt} = \varepsilon_0 A\frac{dE}{dt}$ Step 1: $$ Given Information See problem statement for all…

Problem Statement Solve the fluid mechanics problem: Sunlight of intensity $I = 1400$ W/m² falls on a perfectly absorbing surface. Calculate the radiation pressure exerted on the surface. For perfect absorption, radiation pressure $P = I/c$ For perfect reflection: $P = 2I/c$ Step 1: Since surface is perfectly absorbing: $$P = \frac{I}{c} = \frac{1400} Given…

Problem Statement Determine the electric field for the configuration described: The intensity of sunlight reaching Earth’s surface is $I = 1400$ W/m². Find the amplitude of the electric field $E_0$ in this radiation. $I = \frac{1}{2}\varepsilon_0 c E_0^2 \Rightarrow E_0 = \sqrt{\frac{2I}{\varepsilon_0 c}}$ Step 1: $$E_0 = \sqrt{\frac{2I}{\varepsilon_0 c}} = \sqrt{\frac{2\times1 Given Information See problem…

Problem Statement Solve the oscillation/wave problem: Find the average energy density of an electromagnetic wave whose electric field amplitude is $E_0 = 100$ V/m. Average electric energy density: $u_E = \frac{1}{2}\varepsilon_0 E_0^2/2 = \frac{\varepsilon_0 E_0^2}{4}$ wait, more carefully: $u_E = \frac{1}{2}\varepsilon_0 E_{rms}^2 = \frac{1}{2}\vareps Given Information See problem statement for all given quantities. Physical Concepts…

Problem Statement Solve the magnetic field/force problem: The electric field amplitude in an electromagnetic wave travelling in free space is $E_0 = 50$ N/C. Find the amplitude of the magnetic field $B_0$. In a plane EM wave: $B_0 = E_0/c$ Step 1: The ratio of electric to magnetic amplitudes equals $c$: $$B_0 = \frac{E_0}{c} =…

Problem Statement Calculate the frequency of sodium yellow light with wavelength $\lambda = 589$ nm. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful…

Problem Statement Solve the oscillation/wave problem: An AM radio station broadcasts at a frequency of 1000 kHz. Find the wavelength of the radio wave. $c = f\lambda \Rightarrow \lambda = c/f$ Step 1: $f = 1000\text{ kHz} = 10^6\text{ Hz}$ Step 2: $$\lambda = \frac{c}{f} = \frac{3\times10^8\text{ m/s}}{10^6\text{ Hz}} = 300\text{ m}$$ $$\boxed{\lambda Given Information…

Problem Statement Solve the magnetic field/force problem: Show that the speed of an electromagnetic wave in vacuum is $c = 1/\sqrt{\mu_0 \varepsilon_0}$ and calculate its value given $\mu_0 = 4\pi\times10^{-7}$ T·m/A and $\varepsilon_0 = 8.85\times10^{-12}$ C²/(N·m²). Maxwell’s wave equations give $c = 1/\sqrt{\mu_0\varepsilon_0}$ Step 1: Product $\mu_0\va Given Information $c = 1/$ $c = 1/$…