As shown in the figure, a rectangular loop with a length of 20.0 cm and a width

Question

As shown in the figure, a rectangular loop with a length of 20.0 cm and a width w of 15.0 cm has 20 turns and carries a current of 0.13 A counterclockwise around the loop when viewed from the positive x-axis. A horizontal (parallel to the x-z plane) magnetic field of magnitude 0.023 T is oriented at an angle of 65° relative to the perpendicular to the loop (the positive x-axis). (Assume the length and width are measured along the z and y-axes, respectively.) s x-z plane

1. Find the components of the magnetic force acting on each side of the loop.

Components of the magnetic force acting on the top section of the loop.

FTop, x = N

FTop, y = N

FTop, z = N

Components of the magnetic force acting on the bottom section of the loop.

FBottom, x = N

FBottom, y = N

FBottom, z = N

Components of the magnetic force acting on the left section of the loop.

FLeft, x = N

FLeft, y = N

FLeft, z = N

Components of the magnetic force acting on the right section of the loop.

FRight, x = N

FRight, y = N

FRight, z = N

2. Find the net magnetic force on the loop. (Enter the magnitude only.) FNet = N

3. Find the magnetic torque on the loop. magnitude (N m)

Explanation / Answer

1.

B = magnetic field = 0.023 Cos65 i + 0.023 Sin65 k = 0.00972 i + 0.021 k

Ltop = 0.20 k

i = 0.13 A

Ftop = force on top side = i (Ltop x B) = (0.13) ((0.20 k) x (0.00972 i + 0.021 k )) = 2.53 x 10-4 j N

Ftop,x = 0 N

Ftop,y = 2.53 x 10-4 N

Ftop,z = 0 N

2.

B = magnetic field = 0.023 Cos65 i + 0.023 Sin65 k = 0.00972 i + 0.021 k

Lbottom = - 0.20 k

i = 0.13 A

Ftop = force on top side = i (Ltop x B) = (0.13) ((- 0.20 k) x (0.00972 i + 0.021 k )) = - 2.53 x 10-4 j N

Ftop,x = 0 N

Ftop,y = - 2.53 x 10-4 N

Ftop,z = 0 N

3.

B = magnetic field = 0.023 Cos65 i + 0.023 Sin65 k = 0.00972 i + 0.021 k

Lleft = - 0.20 j

i = 0.13 A

Fleft = force on top side = i (Ltop x B) = (0.13) ((- 0.20 j) x (0.00972 i + 0.021 k )) = (- 5.46 x 10-4) i + 0 j + (2.53 x 10-4)k

Fleft,x = - 5.46 x 10-4 N

Fleft,j = 0 N

Fleft,z = 2.53 x 10-4 N

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