A metal wire \( P Q \) slides on parallel metallic rails having separation \( 0.25 \mathrm{~m} \...

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A metal wire \( P Q \) slides on parallel metallic rails having separation \( 0.25 \mathrm{~m} \), each having negligible resistance. There is a \( 2 \Omega \) resistor and \( 10 \mathrm{~V} \) battery as shown in figure. There is a uniform magnetic field directed into the plane of the paper of magnitude \( 0.5 \mathrm{~T} \). A force of \( 0.5 \mathrm{~N} \) to the left is required to keep the slide wire \( P Q \) moving with constant speed to the right. With what speed is the wire \( P Q \) moving?
(a) \( 14 \mathrm{~m} / \mathrm{s} \)
(b) \( 16 \mathrm{~m} / \mathrm{s} \)
(c) \( 18 \mathrm{~m} / \mathrm{s} \)
(d) \( 144 \mathrm{~m} / \mathrm{s} \)
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