A rectanglular loop consists of 6 turns of wire carrying a current of 3.9 A. The
ID: 1425086 • Letter: A
Question
A rectanglular loop consists of 6 turns of wire carrying a current of 3.9 A. The loop is in the x-y plane, and the direction of flow of the current is shown in the figure. The loop has dimensions a = 1 cm and b = 5 cm. Consider a uniform magnetic field of strength 2.6×10-4 T in x, y, or z directions.
1)
If the uniform field of 2.6×10-4 T is along the +x axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
= ___ N*m
Fa = ___ N
Fb = ___ N
If the uniform field of 2.6×10-4 T is along the +y axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
= ___ N*m
Fa = ___ N
Fb = ___ N
If the uniform field of 2.6×10-4 T is along the +z axis, find the magnitude of the torque acting on the loop and the total force on side a and b.
= ___ N*m
Fa = ___ N
Fb = ___ N
Explanation / Answer
1) magnetic force on current carrying wire =N I L B sin@
B = 2.6 x 10^-4 T i
for a : L = 0.01m j
@ = 90 deg
Fa = 6 x 3.9 x 0.01 x 2.6 x 10^-4 x sin90 = 6.08 x 10^-5 N along z axis
for b : L = 0.05 i
@ = 0 deg
Fb = 0
torque = b x Fa = 0.05 x 6.08 x 10^-5 = 3.04 x 10^-6 N m
2) similarly ,
Fa = 0
Fb = 6 x 3.9 x 0.05 x 2.6 x 10^-4 x sin90 = 3.04 x 10^-4 N along z axis
torque = a x Fb = 0.01 x 3.04 x 10^-4 = 3.04 x 10^-6 N m
3) Fa = 6 x 3.9 x 0.01 x 2.6 x 10^-4 x sin90 = 6.08 x 10^-5 N along x axis
Fb = 6 x 3.9 x 0.05 x 2.6 x 10^-4 x sin90 = 3.04 x 10^-4 N along y axis
torque = (b Fa) + (aFb) = 6.08 x 10^-6 N m