Question

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

Answer 1

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

$\frac{dB}{dt}=\frac{{\mu }_{0}N}{2r}.\frac{di}{dt}=\frac{4\pi \times {10}^{-7}\times 1000}{2\times 2\times {10}^{-2}}.\frac{di}{dt}=\pi \times {10}^{-2}.\frac{di}{dt}$

As $\frac{di}{dt}\approx \frac{\Delta I}{Deltat}=\frac{0.1}{10\times {10}^{-3}}$

$\therefore \frac{dB}{dt}=-\pi$

As $\varphi =NBA=50\times \pi \times ({10}^{-3}{)}^2\times B$

$\therefore E=-\frac{d\varphi }{dt}=-NA\frac{dB}{dt}=-50\times \pi \times ({10}^{-3}{)}^2\times (-\pi )=492.98\times {10}^{-6}=493\mu V$