A Long Vertical Wire Carries a Steady $70 \mathrm {~A}$ Current as Shown in the Figure, a Pair of Horizontal

Multiple Choice

A long vertical wire carries a steady $70 \mathrm {~A}$ current. As shown in the figure, a pair of horizontal rails are $0.20 \mathrm {~m}$ apart. $\mathbf { A } 20 - \Omega$ resistor connects points $a$ and $b$ , at the end of the rails. $\mathbf { A }$ bar is in contact with the rails, and is moved by an external force with a constant horizontal velocity of $0.90 \mathrm {~m} / \mathrm { s }$ to the right, as shown. The bar and the rails have negligible resistance. At the instant that the bar is $0.20 \mathrm {~m}$ from the wire, what are the induced current in the resistor and its direction through the resistor? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) $0.63 \mu \mathrm { A }$ , from $b$ to $a$
B) $0.32 \mu \mathrm { A }$ , from $b$ to $a$
C) $1.9 \mu \mathrm { A }$ , from $b$ to $a$
D) $0.32 \mu \mathrm { A }$ , from $a$ to $b$
E) $0.63 \mu \mathrm { A }$ , from $a$ to $b$