A loop of wire has the shape of a right triangle (see the drawing) and carries a

Question

A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I = 4.50 A. A uniform magnetic field is directed parallel to side AB and has a magnitude of 2.10 T.

(a) Find the magnitude and direction of the magnetic force exerted on each side of the triangle.

(b) Determine the magnitude of the net force exerted on the triangle.
7 N

side AC     1 N directed 2---Select---upwardsdownwardsto the leftto the rightinto the pageout of the page(no force) side CB     3 N directed 4---Select---upwardsdownwardsto the leftto the rightinto the pageout of the page(no force) side BA     5 N directed 6---Select---upwardsdownwardsto the leftto the rightinto the pageout of the page(no force) 55.00 2.00 m

Explanation / Answer

from figure, tan(55) = L_AC/2

==> L_Ac = 2*tan(55)

= 2.856 m

L_BC = sqrt(2^2 + 2.856^2)

= 3.48 m

a) FAc = B*I*L_Ac*sin(theta)

= 2.10*4.50*2.856*sin(90)

= 24.12 N (along -z axis)

b) FCB = B*I*L_CB*sin(theta)

= 2.10*4.50*3.48*sin(55)

= 32.87 N (along +z axis)

c) F_BA = B*I*L_BA*sin(theta)

= 0 (since theta = 180 degrees),

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