Question 1
Consider a long straight conducting wire that terminates in a metal sphere of radius r = 0:50 ± 0:01 cm. Suppose the wire is carrying a current of I = 3:0 ± 0:2 A in order to charge the sphere (positively).
(a) Sketch the shape of the electric and magnetic fi elds around the wire and the sphere.
(b) Discuss the relative merits of using the Biot-Savart law and Ampere's law to calculate the magnetic fi eld around the wire. In this case, is it necessary to include the Maxwell correction to Ampere's law?
(c) Calculate the magnetic field strength at point P, which lies a distance of d = 1:00 ± 0:01 cm from the wire and R = 10:0 ± 0:1 cm from the centre of the ball.
(d) Calculate the uncertainty in the magnetic field strength. Does the fact that this wire is not in nite in extent make a signi cant impact on the results? Explain.
Question 2
A 1.0mW laser beam with a wavelength of λ = 532 nm encounters a double-slit, where the separation between the slits is 50:0μ m. The resulting di raction pattern is observed on a screen 20.0m away.
(a) Draw a diagram(s) of the system including all relevant information. Include what you would expect to see at the slit and at the screen.
(b) What is the distance between the m = +2 and m = 2 di raction orders? List any assumptions you make.
(c) What is the phase di erence between wavefronts originating from the two slits, at a point on the screen located +Π/10m from the zero'th order?
(d) Briefly list the key di erences in the observed di raction pattern if the double-slit were replaced with a di raction grating with the same slit spacing.
The laser beam is now directed into a dilute sample containing spherical, metallic nanoparticles which are 5 nm in diameter.
(e) Would you expect the laser to interact with the nanoparticles? If so how? Justify your answer.
(f) Assume that the nanoparticle is able to absorb photons at 520 nm. At what velocity does the nanoparticle need to move for the photon to be absorbed. Assess your answer.