As shown in the figure, a rectangular loop with a length e of 20.0 cm and a widt
ID: 1585930 • Letter: A
Question
As shown in the figure, a rectangular loop with a length e of 20.0 cm and a width w of 15.0 cm has 20 turns and carries a current of 0.37 A counterclockwise around the loop when viewed from the positive x-axis. A horizontal (parallel to the x-z plane) magnetic field of magnitude 0.031 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.) zplane (a) 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.Explanation / Answer
F(top) x = 0 N
F (top) y = 0.37 A X 20 X10^(-2) mrs X 20 turns X 0.031 T X sin 25 = 1.94 X 10^(-2) N
F top z = 0N
F bot x = 0 N
Fbot y = 0.37A X 20 X10^(-2) mrs X 20 turns X 0.031TX sin(155)
= -1.94 X 10^(-2) N
F bot z = 0 N
Let us consider Left wire
F x = - 0.37A X 15X 10^(-2) X 20 X 0.031 T X cos 25 = - 3.11 X 10^(-2) N
F y = 0 N
Fz = 0.37 A X 15 X 10^(-2) mrs X 20 turns x 0.031 T X cos25 = 1.45 X 10^(-2) N
Now finally right wire
Fx = 0.37 A X 15 X 10^(-2) mrs x 20 turns X 0.031 T X cos25 = 3.11 X 10^(-2) N
Fy = 0 N
Fz = - 0.37 A X 15 X 10^(-2) mrs x 20 turns X 0.031 T X cos65 = - 1.45 X 10^(-2) N
Net force on loop = 0 N
Net Torque on loop = 3.11 X 10^(-2) N X 20 X 10^(-2) mrs = 62.2 X 10 ^(-4) Nt-m = 6.22 X 10^(-3) N-m
Direction of Torque= Clock wise about Y-axis as viewed from + Y-axis
(d) If loop rotates, when angle of loop with reference to B-field reduces to zero ,the torque becomes zero
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