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Chapter 13: Problem 1954

An iron rod of length \(L\) and magnetic moment \(\mathrm{M}\) is bent in the form of a semicircle. Now its magnetic moment will be (a) \(\mathrm{M}\) (b) \((2 \mathrm{M} / \pi)\) (c) \((\mathrm{M} / \pi)\) (d) \(\mathrm{M} \pi\)

Short Answer

Expert verified
The magnetic moment of an iron rod of length L and magnetic moment M remains the same (M) when it is bent in the form of a semicircle because the magnetic moment is an intrinsic property of the material and does not change when the object changes shape. Therefore, the correct answer is (a) M.

Step by step solution

01

Understand the concept of magnetic moment

Magnetic moment is a measure of an object's ability to produce a magnetic field. We are given the magnetic moment of an iron rod (M) when it is straight. Now, we need to find how the magnetic moment changes when the rod is bent into a semicircle.
02

Consider the length of the rod

When the rod is bent into a semicircular shape, the length (L) becomes the circumference of the semicircle. The length of the rod (L) can be related to the radius (r) of the semicircle by using the formula: \[L = \pi r\] Now, we need to analyze how the magnetic moment changes with the shape.
03

Understand the effect of bending on magnetic moment

When an iron rod having magnetic moment M is bent, its magnetic moment remains constant because the magnetic moment is a property intrinsic to the material, and it doesn't change when the object changes shape. Thus, we can say that the magnetic moment of the rod (M) remains the same when it is bent into a semicircular shape.
04

Choose the correct answer

Given that the magnetic moment remains constant when the iron rod is bent, the correct option is: (a) M So, the magnetic moment of the iron rod bent into a semicircular shape is still M.

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Most popular questions from this chapter

Two iclentical short bar magnets, each having magnetic moment \(\mathrm{M}\) are placed a distance of \(2 \mathrm{~d}\) apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is. (a) $\sqrt{2}\left(\mu_{0} / 4 \pi\right)\left(\mathrm{M} / \mathrm{d}^{3}\right)$ (b) $\sqrt{3}\left(\mu_{0} / 4 \pi\right)\left(\mathrm{M} / \mathrm{d}^{3}\right)$ (c) $\sqrt{4}\left(\mu_{0} / 4 \pi\right)\left(\mathrm{M} / \mathrm{d}^{3}\right)$ (d) $\sqrt{5}\left(\mu_{0} / 4 \pi\right)\left(\mathrm{M} / \mathrm{d}^{3}\right)$

In each of the following questions, Match column-I and column-II and select the correct match out of the four given choices.(B) Ammeter (Q) Moderate resistance (C) Voltmeter (R) High, Low or moderate resistance (D) Avometer (S) High resistance (a) $\mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{Q} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{S}$ (b) $\mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{Q} ; \mathrm{C} \rightarrow \mathrm{S} ; \mathrm{D} \rightarrow \mathrm{R}$ (c) $\mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{S}$ (d) $\mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{S} ; \mathrm{D} \rightarrow \mathrm{R}$

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A Galvanometer of resistance \(15 \Omega\) is connected to a battery of 3 volt along with a resistance of \(2950 \Omega\) in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be (a) \(6050 \Omega\) (b) \(4450 \Omega\) (c) \(5050 \Omega\) (d) \(5550 \Omega\)
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