The magnetic field in a region is given by vec B = B 0(( x / a )) hat k . A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity vec v = v 0 hat i . The emf induced in the loop is:

Question

The magnetic field in a region is given by vec B = B 0(( x / a )) hat k . A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity vec v = v 0 hat i . The emf induced in the loop is: <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/48d68b0790ac4551ece60a247241275e-.png" /> (A) ( B 0 v 02 d /2 a ) (B) ( B 0 v 0 d /2 a ) (C) ( B 0 v 0 d 2/ a ) (D) ( B 0 v 0 d 2/2 a )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ae2f5fb1b7c162ea736be1b56048c357-.png" /> E 1=( B 0( x + d )/ a ) v 0 d E 2=( B 0( x )/ a ) v 0 d E net = E 1- E 2 E net =( B 0 v 0 d 2/ a )

Q. The magnetic field in a region is given by $B = B_{0} (\frac{x}{a}) \hat{k}$ . A square loop of side $d$ is placed with its edges along the $x$ and y axes. The loop is moved with a constant velocity $v = v_{0} \hat{i}$ . The emf induced in the loop is:

$\frac{B _{0} v _{0}^{2} d}{2 a}$

$\frac{B _{0} v _{0} d}{2 a}$

$\frac{B _{0} v _{0} d ^{2}}{a}$

$\frac{B _{0} v _{0} d ^{2}}{2 a}$

$E_{1} = \frac{B _{0} ( x + d )}{a} v_{0} d$
$E_{2} = \frac{B _{0} ( x )}{a} v_{0} d$
$E_{n e t} = E_{1} - E_{2}$
$E_{n e t} = \frac{B _{0} v _{0} d ^{2}}{a}$

Q. The magnetic field in a region is given by B=B0​(ax​)k^. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity v=v0​i^. The emf induced in the loop is:

2aB0​v02​d​

2aB0​v0​d​

aB0​v0​d2​

2aB0​v0​d2​