(a) an ideal quantum gas comprises non-interacting identical partieles with discrete quantum states labelled 1, 2, possessing energies e1 for which the occupation numbers are nı, partition function is given by z(t. v,n)- lexр(-b (ms, +п,8, +}. explain why the partition function may be written 1 zgh.(t, v)= 1-exp(-e, ) rl [3 marks] (b) show that the mean occupation number is given by n = еxp (be, ) -1" 1aln z without proof.] [you may use the result n = де; )т. е, (rei) 3 marks] (c) describe the procedure for deriving planck's radiation law: hodo de -и (о, т) do- v псеxp (bho) -1| [4 marks a detailed derivation is not required

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?