Concept

# Problem: A small, 1.70-mm-diameter circular loop with R = 1.40x10-2 Ω is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from + 1.0 A to -1.0 A in 9.00x10-2 s.What is the induced current in the inner loop?Express your answer with the appropriate units.

###### FREE Expert Solution

This problem involves magnetic fields produced by loops and solenoids as well as Fraday's law.

The magnetic field produced by a current loop:

$\overline{){\mathbf{B}}{\mathbf{=}}{\mathbf{N}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{r}}}$

Induced emf/Friday's Law:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{d}{\mathbf{\varphi }}_{\mathbf{B}}}{\mathbf{d}\mathbf{t}}}$

Magnetic flux:

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$

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###### Problem Details

A small, 1.70-mm-diameter circular loop with R = 1.40x10-2 Ω is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from + 1.0 A to -1.0 A in 9.00x10-2 s.

What is the induced current in the inner loop?