Reference no: EM13336273

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 / = 3.0 ± 0.2 A in order to charge the sphere (positively).

(a) Sketch the shape of the electric and magnetic fields 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 field 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 I? = 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 infinite in extent make a significant impact on the results? Explain.

Question 2: 

A 1.0mW laser beam with a wavelength of  λ= 532nm encounters a double-slit, where the separation between the slits is 50:0 μm. The resulting diraction 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 diraction orders? List any assumptions you make.

(c) What is the phase dierence between wavefronts originating from the two slits, at a point on the screen located += Π/10m from the zero'th order?

(d) Brie y list the key dierences in the observed diraction pattern if the double-slit were replaced with a diraction grating with the same slit spacing.

The laser beam is now directed into a dilute sample containing spherical, metallic nanoparticles which are 5nm 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.

 

Question 3.

A coil of wire has a radius of r₁, a resistance of R₁, and contains N₁ turns of wire. It is connected to a voltage source V₁. A second, smaller ring has a radius of r₂, a resistance of R2, and AT₂ turns of wire. Ring 2 is placed in the middle of the Ring 1 such that their centres are concentric as shown in the figure below.

When the switch is initially closed:

(a) What is the strength of the magnetic field E₁ generated by the current in Ring 1?

(b) What is the magnetic flux passing through Ring 2 due to A?

(c) Derive an expression for the induced emf in Ring 2, 6₂? How much current flows in Ring 2 and in which direction?

(d) The current flowing in Ring 2 produces its own magnetic field, which in turn induces an emf in Ring 1, e_l. How much is this? In which direction does this current flow?

Ring 2 is now removed. A solid metal cylinder with the same radius as Ring 2 (and height=radius) is dropped through the middle of Ring 1.

(e) What do you expect to observe as the cylinder falls through the ring? Include times before, during and after the cylinder passes through the ring. Justify your answer and list any assumptions you have to make. Hint: You may want to use some diagrams.

(f) Would you expect the same result if Ring 2 were dropped through the loop? Justify your answer.

----------------------------------

The solution file contains PDF file having the complete solution for Question 1 and Questions 2 and Question 3 including all sub parts.