Generating 3V-5V with magnetic core coil?

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NewtonianAlch
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Hi guys,

I'm wondering whether I'd be able to generate around 3V - 5V with a magnetic coil using a high turn ratio in the presence of a changing magnetic field.

I know guitar coils can generally produce around 500mV - 1V, I wish to generate around 3V -5V even if it is for a very short time in the presence of a small changing magnetic field, say around 30μT in under a second.

What kind of core and how many turns of coil would I need? I have some equations here such as B = ∅/S and V = -N*d∅/dt but it is hard to do this without some experimental data.
 
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