A rigid circular loop of radius r and mass m lies in the x-y plane of a flat table and has a current i flowing in it. At this particular place, the Earth's magnetic field is overset arrow B=Bx hati+Bz hatk . The value of i , so that the loop starts tilting, is

Question

A rigid circular loop of radius r and mass m lies in the x-y plane of a flat table and has a current i flowing in it. At this particular place, the Earth's magnetic field is overset arrow B=Bx hati+Bz hatk . The value of i , so that the loop starts tilting, is (A) (m g/π √Bx2 + B22) (B) (m g/π r Bx) (C) (m g/π r Bz) (D) (m g/π r √Bx Bz)

Tardigrade Admin · Accepted Answer

overset arrow M=i(π r2) hatk , overset arrow B=Bx hati+Bz hatk To start tilting τd u e t o m a s s=τm a g n e t i c |(m g) r|=| overset arrow M × overset arrow B| (m g) (r)=i(π r2)(Bx) i=(m g/π r Bx)

Q. A rigid circular loop of radius $r$ and mass $m$ lies in the $x - y$ plane of a flat table and has a current $i$ flowing in it. At this particular place, the Earth's magnetic field is $B \to = B_{x} \hat{i} + B_{z} \hat{k}$ . The value of $i$ , so that the loop starts tilting, is

$\frac{m g}{π B _{x}^{2} + B _{2}^{2}}$

$\frac{m g}{π r B _{x}}$

$\frac{m g}{π r B _{z}}$

$\frac{m g}{π r B _{x} B _{z}}$

$M \to = i (π r^{2}) \hat{k}$ ,
$B \to = B_{x} \hat{i} + B_{z} \hat{k}$
To start tilting
$τ_{d u e t o ma ss} = τ_{ma g n e t i c}$
$∣ (m g) r ∣ = ∣ ∣ M \to \times B \to ∣ ∣$
$(m g) (r) = i (π r^{2}) (B_{x})$
$i = \frac{m g}{π r B _{x}}$

Q. A rigid circular loop of radius r and mass m lies in the x−y plane of a flat table and has a current i flowing in it. At this particular place, the Earth's magnetic field is B→=Bx​i^+Bz​k^ . The value of i , so that the loop starts tilting, is

πBx2​+B22​​mg​

πrBx​mg​

πrBz​mg​

πrBx​Bz​​mg​