Question

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

Answer 1

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)
`(dV)/(dv) = (d(-v))/(dv)`

`(dV)/(dv) = -1`

b) given

v ( t ) = 4 t + 9

V = (-1)(4t + 9)

`(dV)/(dt) = (d((-1)(4t + 9)))/(dt)`

`(dV)/(dv) = -4`