A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated in the form of Joule heat due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be .........

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(2) the same. Given: N→4N and wire radius a→a/2; the size of the coil and the field are unchanged. Idea: P=(ε²)/R, so find how ε and R each change. Emf: each turn links the same flux, so ε=N(dΦ)/(dt) becomes 4 times larger and ε² becomes 16 times larger. Resistance: R=ρℓ/(π a²). The wire is 4 times longer (4 times the turns) and π a² falls to a quarter, so R becomes 4×4=16 times larger. P'=(16 ε²)/(16 R)=P. So the power dissipated stays the same.

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated in the form of Joule heat due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be .........

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