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By Faraday’s Law, if a conducting wire of length ℓ meters moves at velocity v m/s perpendicular to a magnetic field of strength B (in teslas), a voltage of size V = − B ℓ v is induced in the wire. Assume that B = 2 and ℓ = 0.5 . Calculate dV / dv . Find the rate of change of V with respect to time t if v ( t ) = 4 t + 9

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Answer

given,

conducting wire  length =  ℓ m = 0.5

moves at velocity =  v m/s = v ( t ) = 4 t + 9

magnetic field strength = B  = 2 T

V = − B ℓ v

V = - 2 × 0.5 × v

V = - v

a) [tex]\dfrac{dV}{dv} = \dfrac{d(-v)}{dv}[/tex]

   [tex]\dfrac{dV}{dv} = -1 [/tex]

b) given

    v ( t ) = 4 t + 9

    V = (-1)(4t + 9)

   [tex]\dfrac{dV}{dt} = \dfrac{d((-1)(4t + 9))}{dt}[/tex]

   [tex]\dfrac{dV}{dv} = -4 [/tex]

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