Question

A heart pacing device consists of a coil of $50turns$ & radius $1mm$ just the body with $1000turns$ & radius $2cm,$ placed concentrically and coaxially just outside the body. Calculate the average induced EMF in the internal coil, if a current of a $1A$ in the external coil collapses in $10milliseconds.$

Answer 1

The magnetic field is given as,

$B=\frac{{\mu }_{0}iN}{2r}$

Differentiating the above expression with respect to $t$, we get

$\frac{dB}{dt}=\frac{{\mu }_{0}N}{2r}\left(\frac{di}{dt}\right)$

$=\frac{4\pi \times {10}^{-7}\times 1000}{2\times 2\times {10}^{-2}}\left(\frac{-1}{10\times {10}^{-3}}\right)$

$=-\pi$

The average induced emf is given as,

$e=-NA\frac{dB}{dt}$

$=-50\times [\pi \times {\left({10}^{-3}\right)}^2]\times \left(-\pi \right)$

$=493.48\times {10}^{-6}V$

Thus, the average induced emf in the internal coil is $493.48\times {10}^{-6}V$.