The magnetic field existing in a region is given by vecB=B0(1+(x/1)) hatk. A square loop of edge l and carrying a current i, is placed with its edge parallel to the x-y axes. Find the magnitude of the net magnetic force experienced by the loop

Question

The magnetic field existing in a region is given by vecB=B0(1+(x/1)) hatk. A square loop of edge l and carrying a current i, is placed with its edge parallel to the x-y axes. Find the magnitude of the net magnetic force experienced by the loop (A) (1/2) i B0 l (B) Zero (C) i B0 l (D) 2 i B0 l

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/0008e688f2b048588f9ce178f74f8d91-.png" /> vecB=B0(1+(x/l)) hatk at x=0, B1=B0 hatk at x=I, B2=2 B0 hatk F text net =F2-F1=i l(B2-B1) =i l(2 B0-B0) =i l B0

Q. The magnetic field existing in a region is given by $B = B_{0} (1 + \frac{x}{1}) \hat{k}$ . A square loop of edge $l$ and carrying a current $i$ , is placed with its edge parallel to the $x - y$ axes. Find the magnitude of the net magnetic force experienced by the loop

$\frac{1}{2} i B_{0} l$

Zero

$i B_{0} l$

$2 i B_{0} l$

$B = B_{0} (1 + \frac{x}{l}) \hat{k}$
at $x = 0, B_{1} = B_{0} \hat{k}$
at $x = I, B_{2} = 2 B_{0} \hat{k}$
$F_{net} = F_{2} - F_{1} = i l (B_{2} - B_{1})$
$= i l (2 B_{0} - B_{0})$
$= i l B_{0}$

Q. The magnetic field existing in a region is given by B=B0​(1+1x​)k^. A square loop of edge l and carrying a current i, is placed with its edge parallel to the x−y axes. Find the magnitude of the net magnetic force experienced by the loop

21​iB0​l

Zero

iB0​l

2iB0​l

B=B0​(1+lx​)k^ at x=0,B1​=B0​k^ at x=I,B2​=2B0​k^ Fnet ​=F2​−F1​=il(B2​−B1​) =il(2B0​−B0​) =ilB0​

Q. The magnetic field existing in a region is given by $B = B_{0} (1 + \frac{x}{1}) \hat{k}$ . A square loop of edge $l$ and carrying a current $i$ , is placed with its edge parallel to the $x - y$ axes. Find the magnitude of the net magnetic force experienced by the loop

$\frac{1}{2} i B_{0} l$

$i B_{0} l$

$2 i B_{0} l$

$B = B_{0} (1 + \frac{x}{l}) \hat{k}$
at $x = 0, B_{1} = B_{0} \hat{k}$
at $x = I, B_{2} = 2 B_{0} \hat{k}$
$F_{net} = F_{2} - F_{1} = i l (B_{2} - B_{1})$
$= i l (2 B_{0} - B_{0})$
$= i l B_{0}$