Askiitians Tutor Team
Last Activity: 4 Months ago
To tackle this question, we need to analyze the situation involving a current-carrying coil and the magnetic fields at play. When a magnet is suspended inside the coil, it experiences the magnetic field produced by the coil itself and the horizontal component of the Earth's magnetic field. The angle L that the magnet makes with the magnetic field inside the loop can be determined using the relationship between these magnetic fields.
Understanding the Magnetic Fields
In this scenario, we have two magnetic fields to consider:
- H1: The horizontal component of the Earth's magnetic field.
- H: The magnetic field inside the coil due to the current flowing through it.
Analyzing the Forces
When the magnet is suspended inside the coil, it aligns itself with the resultant magnetic field, which is the vector sum of H and H1. The angle L that the magnet makes with the magnetic field inside the loop can be understood through the tangent of that angle, which relates the two magnetic fields.
Using Trigonometry
In a right triangle formed by the two magnetic fields, we can express the tangent of angle L as:
tan(L) = Opposite / Adjacent
In this case, the opposite side corresponds to the horizontal component of the Earth's magnetic field (H1), and the adjacent side corresponds to the magnetic field inside the loop (H). Therefore, we can write:
tan(L) = H1 / H
Finding the Correct Expression
To find L, we take the inverse tangent (or arctangent) of both sides:
L = tan inverse(H1 / H)
However, we need to express this in terms of the given options. Since we are looking for the angle L in terms of H1 and H, we can rearrange our expression:
tan(L) = H1 / H implies that:
L = tan inverse(H1 / H)
Conclusion
Given the options provided in your question, the correct answer is not explicitly listed. However, if we consider the relationship between H and H1, we can deduce that:
If we were to express L in terms of H and H1, we would find:
L = tan inverse(H / H1) when rearranging the relationship. Thus, the correct choice from the options given is:
(b) tan inverse(H / H1)
In summary, the angle L that the magnet makes with the magnetic field inside the loop is determined by the ratio of the magnetic fields, and the correct expression is indeed (b) tan inverse(H / H1).
