tutorial4 (2) - PC1432 Physics IIE Tutorial 4 Question 1...

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PC1432 Physics IIE: Tutorial 4 Question 1: Toroidal solenoid Figure 1: Toroidal solenoid A certain toroidal solenoid has a rectangular cross section (see Fig. 1 ). It has N uniformly spaced turns, with air inside. Do not assume the the field to be uniform inside the cross section. (a) Show that the magnetic flux through the cross section of the toroid is Φ B = μ 0 Nih 2 π ln parenleftbigg b a parenrightbigg . (1) (b) Show that the inductance of the toroidal solenoid is given by L = μ 0 N 2 h 2 π ln parenleftbigg b a parenrightbigg . (2) (c) The fraction b/a may be written as b a = a + b a a = 1 + b a a . (3) Using the power series expansion ln(1 + z 2 ) = z + z 2 / 2 + . . . valid for | z | < 1, show that when b a a , the inductance is approximately equal to L μ 0 N 2 h ( b a ) 2 πa (4) 1
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Question 2: Polarization I Figure 2: A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water, as seen in the Fig. 2 . The refractive index of the plastic wall is 1.61. If the light that has been
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