explain why its D If released from rest, the current loop will Move upward. Move downward. Rotate clockwise. Rotate counterclockwise. Do something not listed here.
The Correct Answer and Explanation is:
To answer this question thoroughly, we need to consider the behavior of a current-carrying loop placed in a magnetic field. The correct answer is:
D. Rotate counterclockwise.
Explanation (300+ words):
A current loop placed in a magnetic field will experience a torque due to the interaction between the magnetic field and the current flowing through the loop. This principle is based on the Lorentz force, where a current-carrying wire in a magnetic field experiences a force given by: F⃗=I(L⃗×B⃗)\vec{F} = I (\vec{L} \times \vec{B})
Where:
- II is the current,
- L⃗\vec{L} is the vector length of the wire segment,
- B⃗\vec{B} is the magnetic field,
- ×\times represents the vector cross product.
If a rectangular current loop is placed in a uniform magnetic field, different sides of the loop will experience magnetic forces in different directions. Specifically:
- The top and bottom sides (horizontal segments) will experience equal and opposite forces that cancel out in translation, but not in rotation.
- The left and right sides (vertical segments) experience magnetic forces in opposite directions, producing a torque.
This torque tends to rotate the loop, aligning its magnetic moment μ⃗\vec{\mu} with the magnetic field B⃗\vec{B}. The magnetic moment of a current loop is: μ⃗=I⋅A⃗\vec{\mu} = I \cdot \vec{A}
Where A⃗\vec{A} is the area vector (perpendicular to the loop’s plane and following the right-hand rule).
The loop will rotate in a direction that aligns the magnetic moment with the external magnetic field. If the magnetic field points into the page and current flows clockwise when viewed from above, the magnetic moment points downward, opposite the field. The system is in an unstable equilibrium and will rotate counterclockwise to reduce potential energy.
Thus, when released from rest, the loop rotates counterclockwise to align with the magnetic field. Hence, the correct answer is:
D. Rotate counterclockwise