The schematic below depicts a rectangular wire loop with side lengths L and 2L that has an a constant electric current of unknown magnitude I running through it clockwise as indicated by the orange arrows. This wire loop is in a location with a uniform and constant external magnetic field B pointing in the z- direction. The wire loop has a total mass m and is held in a horizontal position (parallel to the z-x-plane) by a rope that is attached to one of the short sides of the loop (labeled side 1 in the schematic). This rope exerts an upward tension force of unknown magnitude Frope. Frope : Fropeŷ top side view ↓ Frope 2L top front view (2 B = B₂ 3 L L 2L (i) [4pts] Find the magnetic force FB on the entire wire loop, by adding up the magnetic forces on each of the four sides: FB,1 FB.2 FB,3 FB.A = ⇒ FB = (ii) [3pts] Use your knowledge of the total force F net on the wire loop to find the unknown tension force Frope. (iii) [10pts] Considering the torque Trope = × Frope imparted on the wire loop (with respect to its center of mass) by the rope and the magnetic torque 7B = μ× B, find an expression for the unknown electric current I using only the given parameters or natural constants.
The schematic below depicts a rectangular wire loop with side lengths L and 2L that has an a constant electric current of unknown magnitude I running through it clockwise as indicated by the orange arrows. This wire loop is in a location with a uniform and constant external magnetic field B pointing in the z- direction. The wire loop has a total mass m and is held in a horizontal position (parallel to the z-x-plane) by a rope that is attached to one of the short sides of the loop (labeled side 1 in the schematic). This rope exerts an upward tension force of unknown magnitude Frope. Frope : Fropeŷ top side view ↓ Frope 2L top front view (2 B = B₂ 3 L L 2L (i) [4pts] Find the magnetic force FB on the entire wire loop, by adding up the magnetic forces on each of the four sides: FB,1 FB.2 FB,3 FB.A = ⇒ FB = (ii) [3pts] Use your knowledge of the total force F net on the wire loop to find the unknown tension force Frope. (iii) [10pts] Considering the torque Trope = × Frope imparted on the wire loop (with respect to its center of mass) by the rope and the magnetic torque 7B = μ× B, find an expression for the unknown electric current I using only the given parameters or natural constants.
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![The schematic below depicts a rectangular wire loop with side lengths L and 2L that has an a constant
electric current of unknown magnitude I running through it clockwise as indicated by the orange arrows.
This wire loop is in a location with a uniform and constant external magnetic field B pointing in the z-
direction. The wire loop has a total mass m and is held in a horizontal position (parallel to the z-x-plane)
by a rope that is attached to one of the short sides of the loop (labeled side 1 in the schematic). This rope
exerts an upward tension force of unknown magnitude Frope.
Frope
: Fropeŷ
top side view
↓
Frope
2L
top front
view
(2
B = B₂
3
L
L
2L
(i) [4pts] Find the magnetic force FB on the entire wire loop, by adding up the magnetic forces on each of
the four sides:
FB,1
FB.2
FB,3
FB.A
=
⇒ FB =
(ii) [3pts] Use your knowledge of the total force F net on the wire loop to find the unknown tension force
Frope.
(iii) [10pts] Considering the torque Trope = × Frope imparted on the wire loop (with respect to its center of
mass) by the rope and the magnetic torque 7B = μ× B, find an expression for the unknown electric current
I using only the given parameters or natural constants.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fc708648b-3b64-4a0a-9613-0716bf3a9dc7%2F1jumx6_processed.png&w=3840&q=75)
Transcribed Image Text:The schematic below depicts a rectangular wire loop with side lengths L and 2L that has an a constant
electric current of unknown magnitude I running through it clockwise as indicated by the orange arrows.
This wire loop is in a location with a uniform and constant external magnetic field B pointing in the z-
direction. The wire loop has a total mass m and is held in a horizontal position (parallel to the z-x-plane)
by a rope that is attached to one of the short sides of the loop (labeled side 1 in the schematic). This rope
exerts an upward tension force of unknown magnitude Frope.
Frope
: Fropeŷ
top side view
↓
Frope
2L
top front
view
(2
B = B₂
3
L
L
2L
(i) [4pts] Find the magnetic force FB on the entire wire loop, by adding up the magnetic forces on each of
the four sides:
FB,1
FB.2
FB,3
FB.A
=
⇒ FB =
(ii) [3pts] Use your knowledge of the total force F net on the wire loop to find the unknown tension force
Frope.
(iii) [10pts] Considering the torque Trope = × Frope imparted on the wire loop (with respect to its center of
mass) by the rope and the magnetic torque 7B = μ× B, find an expression for the unknown electric current
I using only the given parameters or natural constants.
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