Question

Suppose that the magnetic field in some region has the form B = kz ˆx (where k is a constant). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I , flowing counterclockwise, when you look down the x axis.

Answer 1

Answer:

$F = ika^2$

Explanation:

As we know that loop is placed in YZ plane and magnetic field is along x direction

So here net force on the side of the loop which lies along Y axis is given as

$F_1 = i (\vec L \times \vec B)$

here we know that on Y axis z = 0

so B = 0

so we have

$F_1 = 0$

now on the opposite side we have z = a

so magnetic field is given as

$B = ka$

so force on that side is given as

$F = i(\vec L \times \vec B)$

$F = i(a)(ka) sin90$

$F_2 = ika^2$

so net force on the loop is given as

$F = F_1 + F_2$

$F = ika^2$