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# A conductor lies along the $z$-axis at $-1.5 \leq z \leq 1.5\;m$ and carries a fixed current of $10.0\;A$ in $-a_{z}$ direction (see figure). For a field $\bar{B}=3.0 \times 10^{-4} e^{-0.2x} \hat a_y\;T$. Find the power required to move the conductor at constant speed to $x = 2.0m, y = 0\;m\;in\; 5 \times 10–3\; s$. Assume parallel motion along the $x$-axis.

$\begin{array}{1 1}(A)\;14.85\;W \\ (B)\;29.7\;W \\(C)\;1.57\;W \\(D)\;2.97\;W \end{array}$

\begin{align*}P &= \frac{W}{t} \\ & = \frac{14.83 \times 10^{-3}}{5 \times 10^{-3}} \\ & = 2.97 W \; approx\end{align*}
Parallel motion along the $x$-axis $2.97\;W$