The world\'s lightest bird is the bee hummingbird; its mass is 1.6 g (less than
ID: 1436647 • Letter: T
Question
The world's lightest bird is the bee hummingbird; its mass is 1.6 g (less than that of a penny) As shown m (Figure 1). we design a perch for this bird that is supported by a magnetic force The perch is 10 cm long. has a mass of 7 8 g, and contains a wire carrying a current I 4.0 A The perch is 10 cm long has a mass of 7.8 g and contains a wire carrying a current I = 4.0 A. The perch is oriented at right angles to a uniform magnetic field that is just strong enough to support the perch and a boo hummingbird What are the direction and magnitude of the magnetic field? containing the magnetic force F _B and I (that is, the plane of the page). We point our thumb in the current arrow in the direction our fingers cut until it is perpendicular to the plane of the page. direction of B. To find the magnitude of the magnetic field, we apply Newton's second law to the vertical (y)for M = m_bird + m_perch = 16.g + 7.8g = 9.Ag = 9.4. The equilibrium condition, sigma ^F_g = 0, gives F_B - Mg = 0, IIB = M_g, B = Mg/II = (9.4 Times 10 ^-3 kg) (9.8 m/x^2)/(4.0A)(0.100m) = 0.2 Before you think of building this perch for your pet bird, consider what happens as levitation of this sort is used technologically, but with addition systems to ensure stability. How massive a bird could this perch support if the current were increased to I = 4.8 A? Express your answer to two significant figures and includes appropriate units.Explanation / Answer
Since Force due to magnetic field is equal to total weight of perch and the bird.
BIL=(mbird +mperch)g
=>B=(mbird +mperch)g /IL
B =(1.6+7.8)*10-3*9.8/4*0.1
B=0.2303 T
From Right hand rule ,the direction of the magnetic field should be from the viewer into the plane of the picture
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BIL=(mbird +mperch)g
0.2303*4.8*0.1 =(mbird+7.8*10-3)*9.8
mbird=3.48*10-3 kg =3.5*10-3 kg (approx)
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