Electricity and Magnetism Answers

If we add a dielectric material with a dielectric constant k=3.0 between the plates of a fully-charged 2.0μF capacity while a 2 kV supply remains connected (ie, V constant, Q can change), by what factor does it affect the following (ie, is it the same, double, halved, etc)?
i) the electric field,
ii) the capacitance,
iii) the potential energy energy stored in the capacity.
Be sure to justify your answer using the appropriate equation.

a) A freshly prepared sample of a certain radioactive isotope has an activity of 4.70×10^8Bq. After 4.00hours, its activity is 1.90×10^8Bq (1 becquerel = 1 decay per second). Find the decay constant and half-life of the sample.

b) Most solar radiation has a wavelength of 1μm or less. What energy gap should the material in a solar cell have in order to absorb this radiation?

c) The refractive index of moist air in the front of an aircraft is 1.023. Of the LIDAR system detects a return pulse from air resistance (wind shear) after 20.0μs, how far away is the wind shear? Assume the correction for the air speed of the aircraft is negligible.

A coil of wire of area 0.2m^(2) containing 1000 turns is placed in a magnetic field of induction √2T. At time t=0 the axis of the coil and the direction of magnetic field are along z-direction.The coil is rotated by an angle 45° in 2s about y -axis. Assuming the constant angular speed the average e.m.f induced in the coil is approximately
Ans :41.4V

A Time of Flight Mass Spectrometer is a powerful tool utilizing electric fields to determine the mass of ions emitted/ejected from the surface of a sample. As shown in figure 1 below, a laser can be focused onto a sample of ejected ions can be accelerated by an electric field to a high transparency grid after which they continue with a constant velocity to the detector.
If the sample -> grid distance is 10mm and a potential difference of 50 volts is applied between them,
(i) calculate the electric field accelerating the ions.
If negative ions are to be detected as n figure 1 and the grid is grounded.
(ii) what is the potential of the sample with respect to ground?

Electron Diffraction: Describe the diffraction of electrons by a crystalline material. What is the wavelength of an electron? How is the wavelength of the electron controlled? How is crystal lattice spacing determined? You may use equations, sample calculations as examples and diagrams to enhance your description.

Devise a strategy to derive an expression of Electric Field at a point R due to an Electric
Dipole by gausss law or columbs law

an isolated charged point partivle produces elwctric foreld E at 2m away claculate E at 2m away?

A rocket is fired vertically up from rest. If it is designed to maintain a constant upward acceleration of 1.5g, calculate the time t required for it to reach an altitude of 30 km and its velocity at that position.