A conductor lies along the z-axis at –1.5 ≤ z < 1.5 m and carries a fixed current of 10.0 A in direction (see figure). For a field = 3.0 × 10–4 e–0.2x T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10–3 s. Assume parallel motion along the x-axis. [Use e-0.4=0.67]

Engineering

Physics

Motional EMF

Question

A conductor lies along the z-axis at –1.5 ≤ z < 1.5 m and carries a fixed current of 10.0 A in $- {\hat{a}}_{z}$ direction (see figure). For a field $\vec{B}$ = 3.0 × 10^–4 e^–0.2x ${\hat{a}}_{y}$ T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10^–3 s. Assume parallel motion along the x-axis. [Use e^-0.4=0.67]

29.7 W

2.97 W

1.57 W

14.85 W

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F = iℓB

= 10 × 3 × 3 × 10^–4 × e^–0.2x

^{$\int dW = 9 \times 10^{- 3} \int_{0}^{2} e^{0 .2 x} dx$}

^{$P_{av} = \frac{9 \times 10^{- 3} \times {\frac{e^{0 .2 x}}{- 0 .2} |}_{0}^{2}}{t}$}

^{$= \frac{9 \times 10 \times 10^{- 3}}{5 \times 10^{- 3} \times 2} [1 - e^{- 0.4}]$}

^{$= 9 [1 - \frac{1}{e^{2 / 5}}] = 2 . 97 W$}