In a coil of resistance 8 Ω, the magnetic flux due to an external magnetic field varies with time as φ=(2/3)(9- t 2). The value of total heat produced in the coil, till the flux becomes zero, will be J.

Question

In a coil of resistance 8 Ω, the magnetic flux due to an external magnetic field varies with time as φ=(2/3)(9- t 2). The value of total heat produced in the coil, till the flux becomes zero, will be J. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

φ=(2/3)(9- t 2)=0 t =3 sec e =(- d φ/ dt )=-(2/3)(0-2 t )=(4 t /3) Heat produced in 3 sec =∫ ( e 2/ r ) dt =∫ limits03 (16 t 2/9 × 8) dt =2 J

Q. In a coil of resistance $8Ω$ , the magnetic flux due to an external magnetic field varies with time as $ϕ = \frac{2}{3} (9 - t^{2})$ . The value of total heat produced in the coil, till the flux becomes zero, will be _____ $J$ .

$ϕ = \frac{2}{3} (9 - t^{2}) = 0$
$t = 3 sec$
$e = \frac{- d ϕ}{d t} = - \frac{2}{3} (0 - 2 t) = \frac{4 t}{3}$
Heat produced in $3 sec = \int \frac{e ^{2}}{r} d t = 0 \int 3 \frac{16 t ^{2}}{9 \times 8} d t$ $= 2 J$

Q. In a coil of resistance 8Ω, the magnetic flux due to an external magnetic field varies with time as ϕ=32​(9−t2). The value of total heat produced in the coil, till the flux becomes zero, will be _____J.

ϕ=32​(9−t2)=0 t=3sec e=dt−dϕ​=−32​(0−2t)=34t​ Heat produced in 3sec=∫re2​dt=0∫3​9×816t2​dt =2J

Q. In a coil of resistance $8Ω$ , the magnetic flux due to an external magnetic field varies with time as $ϕ = \frac{2}{3} (9 - t^{2})$ . The value of total heat produced in the coil, till the flux becomes zero, will be _____ $J$ .

$ϕ = \frac{2}{3} (9 - t^{2}) = 0$
$t = 3 sec$
$e = \frac{- d ϕ}{d t} = - \frac{2}{3} (0 - 2 t) = \frac{4 t}{3}$
Heat produced in $3 sec = \int \frac{e ^{2}}{r} d t = 0 \int 3 \frac{16 t ^{2}}{9 \times 8} d t$ $= 2 J$