Electromagnetic Waves

- For an electromagnetic wave, the average power passing through an area is given by: where is the speed of light, is the magnetic field amplitude, and is the permittivity of free space.
- The area of the circle is given by .
- Substituting the known values, we get: - Simplifying the expression: Thus, the value of is 12.0.

The fringe separation in Young's double slit experiment is given by: where is the wavelength, is the distance to the screen, and is the slit separation.
Since the kinetic energies are the same for both beams, the velocities of the and molecules will be the same, meaning the de Broglie wavelengths for both beams are the same. Therefore, the ratio of fringe separations for the two cases will be the ratio of the slit separations: The position of the 4 bright fringe for will correspond to the bright fringe for , so we have: Thus, the correct answer is (D) 8.

- The given output waveform suggests a filtering or smoothing action, which is typically achieved by a resistor-capacitor (RC) circuit. The circuit behavior can be determined by analyzing the time constant and the frequency response.
- From the options, the configuration of resistor and capacitor in series fits the expected behavior as described.

To calculate the electric flux through a sphere of radius , we use the definition of electric flux: where is the solid angle element. The flux simplifies to: The integrals over and give: Thus the total flux is: Substituting limits and solving the integral gives the result: This simplifies to: Thus, , which is approximately .

- In the quark model for baryons, the particle has two up quarks and one strange quark. - The wavefunction for the particle will involve a linear combination of quark flavour states. Since the isospin quantum number and strangeness is , the flavour part of the wavefunction involves combinations of , , and states.
- The correct choice is a normalized combination: - This is the flavour wavefunction for the particle.

The fringe width in Young’s double slit experiment is given by: where is the wavelength, is the distance to the screen, and is the slit separation. The wavelength for a transition in the Balmer series is given by: where is the Rydberg constant. For the fringe width to be constant, the slit separation must be scaled by a factor that compensates for the change in as changes. Thus, the required factor for scaling is , which corresponds to option (C).