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A circular loop 40 cm in diameter is made froma flexible conductor and lies at right angles to a uniform 12-T magnetic field. At time t = 0 the loop starts to expand, its radius increasing at the rate of 5.0 mm/s Find the induced emf in the loop: a) at t 1.0 s and b) at t 10 s.

Respuesta :

Answer:

Explanation:

As we know that magnetic flux is given by

[tex]\phi = B.A[/tex]

[tex]\phi = B.\pi r^2[/tex]

now from Faraday's law

[tex]EMF = \frac{d\phi}{dt}[/tex]

[tex]EMF = \frac{d(B. \pi r^2)}{dt}[/tex]

[tex]EMF = 2\pi r B \frac{dr}{dt}[/tex]

now we have

[tex]r = 40/2 = 20 cm[/tex]

B = 12 T

[tex]\frac{dr}{dt} = 5 \times 10^{-3} m/s[/tex]

Part a)

now at t = 1 s

r = 20 + 0.5 = 20.5 cm

[tex]EMF = (2\pi (0.205))(12)(5 \times 10^{-3})[/tex]

[tex]EMF = 0.077 Volts[/tex]

Part b)

now at t = 10 s

r = 20 + 0.5(10) = 25 cm

[tex]EMF = (2\pi (0.25))(12)(5 \times 10^{-3})[/tex]

[tex]EMF = 0.094 Volts[/tex]

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