Consider a circular solenoid with a diameter of 20.0 cm creating a magnetic field that increases at the rate of 0.0500 T/s. 

i) For a circular cross-section with a diameter of 12 cm centered on the solenoid axis and perpendicular to the solenoid axis, find the rate of change of flux through the circle.

ii) Calculate the magnitude of the induced electric field at a radial distance of 6 cm from the solenoid axis. 

iii) Determine the magnitude of the induced electric field at a radial distance of 12 cm from the solenoid axis.

A photon sail is a hypothetical propulsion system that generates thrust by reflecting light off a large, lightweight sail. Consider a powerful source of monochromatic light directed at a space shuttle's photon sail as it travels in a straight line between two planets separated by 47.6 × 10 ⁶ km. Determine the shuttle's speed if the journey takes 6.5 days.

To achieve a de Broglie wavelength of 530 nm, what potential difference is required to accelerate an electron from a state of rest?

Consider a bowling ball with a mass of 0.3 kg moving at a speed of 15 m/s. What is the de Broglie wavelength associated with this moving ball?

An electron is trapped in a 1D box of length 4.0 nm. Determine the quantum number if the electron exhibits a de Broglie wavelength of 2.0 nm.