A uniform conducting rectangular loop of sides l, b and mass m carrying current i is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of loop. The value of tension which is least is

Question

A uniform conducting rectangular loop of sides l, b and mass m carrying current i is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of loop. The value of tension which is least is (A) (m g-B b/2) (B) (m g+B b/2) (C) (m g-2 i B b/2) (D) (m g+2 B b/2)

Tardigrade Admin · Accepted Answer

Taking moments about point B to be zero. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6e71e5b87ae23ed6bbf327340400486f-.png" /> T1 ℓ+i b ℓ B=m g (ℓ/2) ; T1=(m g-2 i b B/2)

Q. A uniform conducting rectangular loop of sides $l, b$ and mass $m$ carrying current $i$ is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field $B$ which is parallel to the longer side of loop. The value of tension which is least is

$\frac{m g - B b}{2}$

$\frac{m g + B b}{2}$

$\frac{m g - 2 i B b}{2}$

$\frac{m g + 2 B b}{2}$

Taking moments about point $B$ to be zero.

$T_{1} ℓ + ib ℓ B = m g \frac{ℓ}{2}; T_{1} = \frac{m g - 2 ib B}{2}$

Q. A uniform conducting rectangular loop of sides l,b and mass m carrying current i is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of loop. The value of tension which is least is

2mg−Bb​

2mg+Bb​

2mg−2iBb​

2mg+2Bb​