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Answer 1

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✍Yes, induced current in loop doesn't depend on size of the wire or of the loop as m, p and d all are constant.

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EXPLANATION —

↪Actually welcome to the concept of electromagnetic induction

See attachment

Here m, p and d all are constant

 Hence proved current is indendent on wire area.

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Answer 2

Answer:

The induced emf will have the same magnitude as the rate of change of magnetic flux through the loop.

|ξ| = |dΦ/dt|

The magnetic flux is the area of the loop times the component of the magnetic field passing perpendicularly through this loop.

Φ = A . B

Assuming the magnetic field (and, thus, its rate of change) is perpendicular to the plane of the loop,

|ξ| = A |dB/dt|

By Ohm's Law, ξ = iR.

iR = A(dB/dt)

The copper will form a wire with some length L and some cross-sectional area a. The resistance R of the wire would be R = pL/a.

i(pL/a) = A(dB/dt)

Find a relation between the length of the loop and its area A.

A = πR²

A = π(L/(2π))²

A = L²/(4π)

i(pL/a) = [L²/(4π)](dB/dt)

i(p/a) = [L/(4π)](dB/dt)

The volume of metal is V = aL

i(p/a) = [L/(4π)](dB/dt)

i = [(aL)/(4πp)](dB/dt)

i = [V/(4πp)](dB/dt)

Density d = m/V.

i = [(m/d)/(4πp)](dB/dt)

i = [m/(4πpd)](dB/dt)

=> Thus, the induced current current does not depends on the size of the wire of loop.