Magnetic Effects Of Current Question 12
Question 12 - 2024 (31 Jan Shift 1)
A coil is placed perpendicular to a magnetic field of $5000 \mathrm{~T}$. When the field is changed to $3000 \mathrm{~T}$ in $2 \mathrm{~s}$, an induced emf of $22 \mathrm{~V}$ is produced in the coil. If the diameter of the coil is $0.02 \mathrm{~m}$, then the number of turns in the coil is :
(1) 7
(2) 70
(3) 35
(4) 140
Show Answer
Answer: (2)
Solution:
$\varepsilon=\mathrm{N}\left(\frac{\Delta \phi}{\mathrm{t}}\right)$
$\Delta \phi=(\Delta \mathrm{B}) \mathrm{A}$
$\mathrm{B}_{\mathrm{i}}=5000 \mathrm{~T}$,
$\mathrm{B}_{\mathrm{f}}=3000 \mathrm{~T}$
$\mathrm{d}=0.02 \mathrm{~m}$
$\mathrm{r}=0.01 \mathrm{~m}$
$\Delta \phi=(\Delta \mathrm{B}) \mathrm{A}$
$=(2000) \pi(0.01)^{2}=0.2 \pi$
$\varepsilon=\mathrm{N}\left(\frac{\Delta \phi}{\mathrm{t}}\right) \Rightarrow 22=\mathrm{N}\left(\frac{0.2 \pi}{2}\right)$
$\mathrm{N}=70$
