Download Phase Sensitive Faraday rotation

Q 15. Using the binomial expansion (1 + z)n = 1 + nz + n(n−1)
+ . . ., show that
2!
Eq. (51) can also be written as,
B =
µo N i
(1 + c4 z 4 + c6 z 6 + ...),
2a
(53)
where, c4 = 15/8a4 and c6 = −105/48a6 .
Q 16. What do you conclude from equation (53) about the uniformity of the
magnetic field? How does the field in the middle of the coils compare with the
field in the center of a single circular loop of the same radius?
Function generator
DC supply
Audio amplifier
Gaussmeter
Helmholtz coil
Figure 14: Instruments for creating and detecting the oscillating magnetic field.
In our experiment, the Helmholtz coil is constructed from 18 gauge copper wire
(diameter 1.2 mm). Each multilayer coil consists of 18 turns in 18 layers, the coil’s
outer and inner diameters are 10.2 cm and 6.5 cm respectively. The length of each
coil is 2.7 cm and radius is 4.5 cm. Inductance of the coils, determined using the
LCR meter, is found to be 7 mH with a resistance of 1.5 Ω for each coil, so the
total inductance of the Helmholtz pair is 15 mH and the total resistance is 3 Ω .
The Helmholtz coil pair constitutes a series RLC circuit. At resonating frequency
ωr , the inductive reactance XL is equal to the capacitive reactance XL and total
impedance is purely resistive. The resonating frequency is,
√
1
ωr =
LC
or
fr =
1
√
.
2π (LC)
20