Respuesta :
Answer:
(A) The area of coil must be = 17.9 [tex]m^{2}[/tex]
(B) Â Maximum translation speed of a point is = 7.5 [tex]\frac{m}{s}[/tex]
Explanation:
Given :
Magnetic field [tex]B = 8 \times 10^{-5}[/tex] T
Induced emf = 9 V
Angular frequency [tex]\omega =[/tex] [tex]2\pi f[/tex]
No. of turns [tex]N = 2000[/tex]
Where [tex]f = \frac{30}{60} = \frac{1}{2}[/tex] so [tex]\omega = \pi[/tex]
(A)
From the laws of electromagnetic induction,
Induced emf = [tex]- N\frac{d \phi}{dt}[/tex]
Where [tex]\phi =[/tex] magnetic flux, in our case magnetic flux [tex]\phi = BA \cos \omega t[/tex]
Max. induced emf = [tex]N \omega BA[/tex]
Therefore area of loop is given by,
  [tex]A = \frac{9 }{2000 \times \pi \times 8 \times 10^{-5} }[/tex]
  [tex]A = 17.9[/tex] [tex]m^{2}[/tex]
(B)
Coil is circular so maximum translation speed is given by,
  [tex]v = r \omega[/tex]
Where [tex]r =[/tex] radius of circle [tex]r = \sqrt{\frac{A}{\pi } }[/tex]
  [tex]v = \sqrt{\frac{A}{\pi } } \omega[/tex]
  [tex]v = \sqrt{\frac{17.9}{\pi } } \pi[/tex]
  [tex]v = 7.5[/tex] [tex]\frac{m}{s}[/tex]
