Answer:
Zero
Explanation:
The electromotive force induced in the loop is given by
[tex]\epsilon=-\frac{d\Phi}{dt}[/tex]
where
[tex]\frac{d\Phi}{dt}[/tex] is the rate of change of magnetic flux through the coil.
The magnetic flux through the coil is given by
[tex]\Phi = BA cos \theta[/tex]
where
B is the magnetic field intensity
A is the area enclosed by the coil
[tex]\theta[/tex] is the angle between the direction of B and the normal to the area of the coil
In this problem, the coil is moving parallel to the current in the wire. Let's remind that the magnetic field produced by a wire is
[tex]B=\frac{\mu_0 I}{2 \pi r}[/tex]
where I is the current in the wire and r is the distance from the wire. In this problem, the loop is moving parallel to the wire, so r remains constant: this means that the magnetic field intensity, B, remains constant.
Also, the area of the coil (A) does not change, neither does [tex]\theta[/tex] since the orientation of the coil remains the same. This means that the magnetic flux through the coil, [tex]\Phi[/tex], does not change: as a result, the emf induced in the coil is zero, and so there is no current induced in the loop.
