A Conducting Rod Whose Length Is $\ell = 1.60 \mathrm {~m}$

A conducting rod whose length is $\ell = 1.60 \mathrm {~m}$ is placed on frictionless $U$ -shaped metal rails that is connected to a lightbulb having a resistance of $4.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $2.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of $6.00 \mathrm {~m} / \mathrm { s }$ ?

A) $10.6 \mathrm {~N}$
B) $18.6 \mathrm {~N}$
C) $8.60 \mathrm {~N}$
D) $12.6 \mathrm {~N}$
E) $9.30 \mathrm {~N}$