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 29 ms . The coil has 85 turns of wire and a diameter of 2.0 mm . The fly is immersed in a magnetic field of magnitude 0.10 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.

Answer 1

Induced EMF is given by:

EMF = -N*d(phi)/dt = -N*(phi_final - phi_initial)/dt

Since given that final magnetic flux = 0, And

phi = Magnetic flux = B*A

So, EMF = -N*(0 - B*A)/dt = N*A*dB/dt

N = 85 turns

A = area = pi*d^2/4 = pi*(2.0*10^-3)^2/4

dt = time interval = 29 ms = 29*10^-3 sec

B = Initial magnetic field = 0.10 mT = 0.10*10^-3 T, So

So,

EMF = 85*0.10*10^-3*pi*(2.0*10^-3)^2/(4*29*10^-3)

EMF = 9.21*10^-7 V = 0.92*10^-6 V = 0.92 V = Induced emf

Let me know if you've any query.