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:
Sure! To fully explain why the correct answer is D: Rotate counterclockwise, let’s break down the physics involved step-by-step.
Context:
This question involves a current-carrying loop placed in a magnetic field and then released from rest. The question asks what the loop will do immediately after being released.
Key concepts:
- Magnetic Force on a Current Loop:
A current loop placed in a magnetic field experiences a force and torque due to the interaction between the magnetic field and the magnetic dipole moment created by the current in the loop. - Magnetic Dipole Moment ($\vec{\mu}$):
The current loop behaves like a magnetic dipole, with a magnetic moment $\vec{\mu}$ proportional to the current and the area vector of the loop (direction given by the right-hand rule). - Torque on a Current Loop:
The torque $\vec{\tau}$ on a current loop in a uniform magnetic field $\vec{B}$ is: $$
\vec{\tau} = \vec{\mu} \times \vec{B}
$$ This torque tends to rotate the loop so that $\vec{\mu}$ aligns with $\vec{B}$.
Why the loop will rotate and not move upward or downward:
- Force vs. Torque:
While individual segments of the loop experience magnetic forces, the net force on a symmetrical loop in a uniform magnetic field is zero (forces on opposite sides cancel out).
However, these forces create a net torque, causing the loop to rotate rather than translate (move upward or downward).
Why it rotates counterclockwise:
- The direction of rotation depends on the directions of $\vec{\mu}$ and $\vec{B}$.
- Using the right-hand rule, the magnetic moment points perpendicular to the loop plane.
- When the loop is not aligned with the magnetic field, the torque acts to rotate it toward alignment.
- The direction of this torque vector (given by $\vec{\mu} \times \vec{B}$) determines the rotation direction (clockwise or counterclockwise).
If the torque vector points out of the page, the loop rotates counterclockwise; if into the page, it rotates clockwise.
In this scenario, given the orientation, the torque causes a counterclockwise rotation.
Summary:
- The loop does not translate up or down because the net magnetic force is zero in a uniform magnetic field.
- The loop experiences torque due to $\vec{\tau} = \vec{\mu} \times \vec{B}$, causing it to rotate.
- The direction of torque leads to a counterclockwise rotation.
- Therefore, the correct answer is D: Rotate counterclockwise.
If you want, I can also explain this with diagrams or vector illustrations—just let me know!