PA04 June 2003 part B
Answer all questions.
You are advised to spend approximately one hour on this section.

1         A microwave transmitter directs waves towards a metal plate. When a microwave detector is moved along a line normal to the transmitter and the plate, it passes through a sequence of equally spaced maxima and minima of intensity.

(a)     Explain how these maxima and minima are formed.
You may be awarded marks for the quality of written communication in your answer                                                                                                                             (4 marks)

            (b)      The detector is placed at a position where the intensity is a minimum. When it is moved a distance of 144 mm it passes through nine maxima and reaches the ninth minimum from the starting point.

Calculate
(i)  the wavelength of the microwaves.  
(ii) the frequency of the microwave transmitter.                                                       (3 marks)

2          Communications satellites are usually placed in a geo-synchronous orbit. 

    (a)     State two features of a geo-synchronous orbit.
                                                                                                                    (2 marks) 

    (b)     Given that the mass of the Earth is 6.00 x 10⁴ kg and its mean radius is 6.40 x 10⁶m,

            (i)     show that the radius of a geo-synchronous orbit must be 4.23 x 10⁷ m

            (ii)    calculate the increase in potential energy of a satellite of mass 750 kg when it is raised from the Earth’s surface into a geo-synchronous orbit.

(6 marks)

3          (a)   The equation F = BIl, where the symbols have their usual meanings, gives the magnetic force that acts on a conductor in a magnetic field.

                   Give the unit of each of the quantities in the equation.

                  F 
B
I
l               

                   State the condition under which the equation applies.

(2 marks)

(b)        The diagram shows a horizontal copper bar of 25 mm x 25mm square cross-section and length l carrying a current of 65 A.

 (i)   Calculate the minimum value of the flux density of the magnetic field in which it should be placed if its weight is to be supported by the magnetic force that acts on it.

           density of copper = 8.9 x 10³kgm^-3

 (ii)     Draw an arrow on the diagram above to show the direction in which the magnetic field should be applied if your calculation in part (i) is to be valid. Label this arrow M.

(5 marks)

4   (a) With reference to the process of nuclear fusion, explain why energy is released when two small nuclei join together, and why it is difficult to make two nuclei come together.
You may be awarded marks for the quality of written communication in your answer.

(3 marks)

(b)        A fusion reaction takes place when two deuterium nuclei join, as represented by
                           ²₁ H   +  ²₁ H   à   ³₂ He  +  ¹₀ n

                   mass of ²H nucleus        = 2.01355 u
mass of ³He nucleus       = 3.01493 u
mass of neutron             = 1.00867 u

           Calculate
 (i)     the mass difference produced when two deuterium nuclei undergo fusion,
 (ii)    the energy released, in J, when this reaction takes place.

(3 marks)