There exist a time varying magnetic field B=α t in a cylindrical region of radius ' a '. An equilateral triangular loop of side l is placed inside the magnetic field as shown. Its sides A B, B C and C A have resistances ' R ', '2R' and '3R' respectively. The magnitude of potential difference across the path A B is

Question

There exist a time varying magnetic field B=α t in a cylindrical region of radius ' a '. An equilateral triangular loop of side l is placed inside the magnetic field as shown. Its sides A B, B C and C A have resistances ' R ', '2R' and '3R' respectively. The magnitude of potential difference across the path A B is (A) (l2 α/2) (B) (l2 α/2 √3) (C) (l2 α/8 √3) (D) (l2 α/4 √3)

Tardigrade Admin · Accepted Answer

emf =(√3 l 2/4) ( dB / dt )=(√3 l 2 α/4) i=(e m f/6 R)=(√3 l2 α/24 R) E l=(1/3) (√3 l2 α/4)-i R =(l2 α/4 √3)-(√3 l2 α/24) =(l2 α/8 √3)

$\frac{l ^{2} α}{2}$

$\frac{l ^{2} α}{2 3}$

$\frac{l ^{2} α}{8 3}$

$\frac{l ^{2} α}{4 3}$

$e m f = \frac{3 l ^{2}}{4} \frac{d B}{d t} = \frac{3 l ^{2} α}{4}$
$i = \frac{e m f}{6 R} = \frac{3 l ^{2} α}{24 R}$
$El = \frac{1}{3} \frac{3 l ^{2} α}{4} - i R$
$= \frac{l ^{2} α}{4 3} - \frac{3 l ^{2} α}{24}$
$= \frac{l ^{2} α}{8 3}$

2l2α​

23​l2α​

83​l2α​

43​l2α​

emf=43​l2​dtdB​=43​l2α​ i=6Remf​=24R3​l2α​ El=31​43​l2α​−iR =43​l2α​−243​l2α​ =83​l2α​

$\frac{l ^{2} α}{2}$

$\frac{l ^{2} α}{2 3}$

$\frac{l ^{2} α}{8 3}$

$\frac{l ^{2} α}{4 3}$

$e m f = \frac{3 l ^{2}}{4} \frac{d B}{d t} = \frac{3 l ^{2} α}{4}$
$i = \frac{e m f}{6 R} = \frac{3 l ^{2} α}{24 R}$
$El = \frac{1}{3} \frac{3 l ^{2} α}{4} - i R$
$= \frac{l ^{2} α}{4 3} - \frac{3 l ^{2} α}{24}$
$= \frac{l ^{2} α}{8 3}$