When a magnet is moved into a wire coil, voltage is induced. if the coil had twice as many loops, the voltage induced would be?

This concept is applicable to how transformers work. Transformers are used to distribute energy at very high voltages. It works through the concept of electromagnetism. The coils of the transformer is where the current passes producing a magnetic field. This magnetic field induces voltage on the other coil. The pattern goes on and that's how they transfer electricity through each other. The equation for the number of coils (N) and the induced voltage (V) is through ratio and proportion:

N₁/N₂ = V₁/V₂

So, if N₂=N₁, then

N₁/2N₁ = V₁/V₂

Cancelling N₁ yields,

1/2 = V₁/V₂

V₂ = 2V₁

Therefore, the induced voltage will be twice as much.