Researchers have tracked the head and body movements of several flying insects,

Question

Researchers have tracked the head and body movements of several flying insects, including blowflies, hover flies, and honeybees. They attach lightweight, flexible wires to a small metal coil on the insect's head, and another on its thorax, and then allow it to fly in a stationary magnetic field. As the coils move through the field, they experience induced emfs that can be analyzed by computer to determine the corresponding orientation of the head and thorax. Suppose the fly turns through an angle of 90 in 27 ms . The coil has 98 turns of wire and a diameter of 2.1 mm . The fly is immersed in a magnetic field of magnitude 0.11 mT .

If the magnetic flux through one of the coils on the insect goes from a maximum to zero during this maneuver find the magnitude of the induced emf.

Explanation / Answer

Use the formula Emf= -N ( change in magnetic flux)/ (change in time)
Recall magnetic flux = Bcos(theta)A
N = 98
d = 2.1 mm

r = 1.05 x 10^-3 m

A= pi r^2 = 3.14 x (1.05 x 10^-3)^2 = 3.46 x 10^-6 m^2
B= 0.11 x 10^-3 T
Theta final is 90... cos90= 0
theta initial is 0...cos0=1
delta theta equals -1
delta time equals 27 ms = 27 x 10^-3 sec

magnetic flux = 0.11 x 10^-3 x 3.46 x 10^-6 x (-1) = 0.3806 x 10^-9

Emf = (98 x 0.3806 x 10^-9) / (27 x 10^-3)

Emf = 1.38 x 10^-6 V

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