Question

A current with sinusoidal time-dependence, whose peak value is 6.55 A and frequency is 671 cycles per second, passes through a long straight wire. A rectangular 18.2 cm

Answer 1

first we have to calculate the fem induced on the rectangualr loop:

$\epsilon = \frac{d\phi}{dt}$

where:

$\phi = \int_r^{r + a} Bbdr = \int_r^{r + a} \frac{\mu_0I_0\sin(\omega t)}{2\pi r}bdr =$

we havbe the flux as fucntion of time:

$\phi = \frac{\mu_0I_0 b\sin(\omega t) }{2\pi}\ln\frac{r +a}{r}$

the induced emf is:

$\epsilon= \frac{d\phi}{dt}= \frac{\mu_0I_0\omega b\cos(\omega t) }{2\pi}\ln\frac{r +a}{r}$

where I0 = 6.55 A w = 2pi f = 671

r = 0.202 m a = 0.182 m and b = 0.0819 m

the power dissipated is:

$P = \epsilon^2/R$