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Chapter 15: Problem 29

A current-carrying conductor is looped into a circle of radius \(10 \mathrm{~cm}\). The magnetic moment of the current loop becomes \(0.314 \mathrm{~A} / \mathrm{m}^{2}\). What is the current in the loop? (A) \(5 \mathrm{~A}\) (B) \(8 \mathrm{~A}\) (C) \(10 \mathrm{~A}\) (D) \(12 \mathrm{~A}\)

Short Answer

Expert verified
(C) \(10 \mathrm{~A}\)

Step by step solution

01

Write the formula for magnetic moment and area of a circle

The given formula for magnetic moment in a loop is: \[M = IA\] And the area of a circular loop is: \[A = \pi r^2\]
02

Substitute the area formula into the magnetic moment formula.

Now, replace A in the magnetic moment formula with the expression from the area of a circle formula: \[M = I(\pi r^2)\]
03

Solve for current, I

Now, rearrange the equation to isolate the current (I) on one side: \[I = \frac{M}{\pi r^2}\]
04

Input given values and calculate the current

Now we input the values for the magnetic moment (M) and radius (r) from the question into the formula: \[I = \frac{0.314 \mathrm{A}/ \mathrm{m}^2}{\pi (0.1\mathrm{m})^2}\] Evaluating this expression, we get: \[I \approx 10 \mathrm{A}\] Now, looking at the available options, we can clearly see that the answer is: (C) \(10 \mathrm{~A}\)

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Most popular questions from this chapter

A current \(i\) ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is [2004] (A) \(\frac{\mu_{0}}{4 \pi}, \frac{2 i}{r} \mathrm{~T}\) (B) Zero (C) Infinite (D) \(\frac{2 i}{r} \mathrm{~T}\)

Two short bar magnets of magnetic moments \(M\) each are arranged at the opposite corners of a square of side \(d\) such that their centres coincide with the corners and their axes are parallel. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is (A) \(\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}\) (B) \(\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}\) (C) \(\frac{\mu_{0}}{4 \pi} \frac{M}{2 d^{3}}\) (D) \(\frac{\mu_{0}}{4 \pi} \frac{M^{2}}{2 d^{3}}\)

A long straight wire of radius a carries a steady current \(i\). The current is uniformly distributed across its cross-section. The ratio of the magnetic field at \(a / 2\) and \(2 a\) is \(\quad\) [2007] (A) \(\frac{1}{2}\) (B) \(\frac{1}{4}\) (C) \(\underline{4}\) (D) 1

A coil in the shape of an equilateral triangle of side \(0.02 \mathrm{~m}\) is suspended from vertex such that it is hanging in a vertical plane between the pole-pieces of a permanent magnet producing a horizontal magnetic field of \(5 \times 10^{-2} \mathrm{~T}\). Current in loop is \(0.1 \mathrm{~A}\). Then (A) magnetic moment of the loop is \(\sqrt{3} \times 10^{-5} \mathrm{~A} / \mathrm{m}^{2}\). (B) magnetic moment of the loop is \(1 \times 10^{-6} \mathrm{~A} / \mathrm{m}^{2}\). (C) couple acting on the coil is \(5 \sqrt{3} \times 10^{-7} \mathrm{~N} / \mathrm{m}\). (D) couple acting on the coil is \(\sqrt{3} \times 10^{-7} \mathrm{~N} / \mathrm{m}\).

Earth's magnetic induction at a certain point is \(7 \times 10^{-5}\) \(\mathrm{Wb} / \mathrm{m}^{2}\). This field is to be annulled by the magnetic induction at the centre of a circular conducing loop \(5.0 \mathrm{~cm}\) in radius. The required current is (A) \(0.056 \mathrm{~A}\) (B) \(6.5 \mathrm{~A}\) (C) \(5.6 \mathrm{~A}\) (D) \(12.8 \mathrm{~A}\)
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