- #1
SilversGodot
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- Homework Statement
- A current-carrying loop with a diameter of 1.0 cm is in a constant magnetic field of 0.5 μT into the page experiencing no torque. What must be the current flowing through the wire?
Hint: there may be multiple correct answers
A. 4.0mA, CCW
B. 4.0mA, CW
C. 0.40A, CCW
D. 0.40A,CW
E. 2.0mA, CCW
F. 2.0mA, CW
- Relevant Equations
- [tex] T = N \ I \ A \ B \ \sin(\theta) = M \ B \ \sin(\theta)\ \text{, }
\ \ \ \text{ or } \ \ \
\vec{T} = N \ I \ \vec{A} \times \vec{B} = \vec{M} \times \vec{B}[/tex]
Disclaimer: The solution to this question has already been posted by my instructor. I made this post to understand why my solution is wrong or if the instructor is wrong, since their explanation does not make sense to me.
My reasoning:
Using the fact that the magnetic torque on a current-carrying loop is
T = N \ I \ A \ B \ \sin(\theta) = M \ B \ \sin(\theta)
and that the torque is 0, I deduced that θ must be either 0 or π rad, since all other variables are non-zero (the number of loops N is 1, the problem assumes a current I, the loop has non-zero area A, and there is an external magnetic field B). Thus, it should not be possible to determine the current and all six options are equally likely. My answer would be options A-F.
The instructor's reasoning:
"Direction is determined via the right hand rule. My thumb points in the direction of the magnetic field (into the page) and my fingers curl in the direction of the current (CW). Since there is no net torque when the field is perpendicular to the loop, the current can flow either CW or CCW and still have no net torque." They gave the work below:
B = \frac{\mu_0I}{2R} \rightarrow I = \frac{2BR}{\mu_0} = 4.0 mA
The instructor marked the A and B were both correct/possible answers.
From what I can tell, the instructor interpreted that the loop is generating the magnetic field given in the problem. From the wording, I assumed that the magnetic field was external to the loop, since it said "in a constant magnetic field," which would imply that something else is causing the field. Additionally, the answer that the current can be either CW or CCW contradicts the fact that they used the right-hand rule. My question for this post is "Is my reasoning wrong? If it is wrong, why?"
My reasoning:
Using the fact that the magnetic torque on a current-carrying loop is
T = N \ I \ A \ B \ \sin(\theta) = M \ B \ \sin(\theta)
and that the torque is 0, I deduced that θ must be either 0 or π rad, since all other variables are non-zero (the number of loops N is 1, the problem assumes a current I, the loop has non-zero area A, and there is an external magnetic field B). Thus, it should not be possible to determine the current and all six options are equally likely. My answer would be options A-F.
The instructor's reasoning:
"Direction is determined via the right hand rule. My thumb points in the direction of the magnetic field (into the page) and my fingers curl in the direction of the current (CW). Since there is no net torque when the field is perpendicular to the loop, the current can flow either CW or CCW and still have no net torque." They gave the work below:
B = \frac{\mu_0I}{2R} \rightarrow I = \frac{2BR}{\mu_0} = 4.0 mA
The instructor marked the A and B were both correct/possible answers.
From what I can tell, the instructor interpreted that the loop is generating the magnetic field given in the problem. From the wording, I assumed that the magnetic field was external to the loop, since it said "in a constant magnetic field," which would imply that something else is causing the field. Additionally, the answer that the current can be either CW or CCW contradicts the fact that they used the right-hand rule. My question for this post is "Is my reasoning wrong? If it is wrong, why?"
