Increase emf received from a coil without changing flux source
Look at current transformers:


Source: 

https://www.electronics-tutorials.ws/transformer/current-transformer.html

Remember that the magnetic field of a wire flows with the right hand rule with the magnetic field flowing in a circle around the wire:


Source: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

Building a coil directly around a wire like the helix method will have some downsides, the magnetic field lines running through the coil will be perpendicular to the coil. In other words the coil won't pick up much magnetic field and the current will be close to zero. 

So build a coil perpendicular to the field lines, like the current transformer.