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Chapter 13: Problem 1958

If a magnet of pole strength \(\mathrm{m}\) is divided into four parts such that the length and width of each part is half that of initial one, then the pole strength of each part will be (a) \((\mathrm{m} / 4)\) (b) \((\mathrm{m} / 2)\) (c) \((\mathrm{m} / 8)\) (d) \(4 \mathrm{~m}\)

Short Answer

Expert verified
The pole strength of each part will be (a) \(\frac{m}{4}\).

Step by step solution

01

Understand the concept of pole strength

Pole strength is a measure of the strength of a magnetic pole in a magnet. It is directly proportional to the product of the magnet's length, width and thickness. In our problem, we have a magnet with a given pole strength m, and we are asked to find the pole strength of each of the four parts after dividing the magnet.
02

Determine the relationship between the pole strength and size of the magnet

Let the lengths of the original magnet be L (length), W (width), and the pole strength be m. When the magnet is divided into four parts, the dimensions of each part will be L/2 (length) and W/2 (width).
03

Calculate the pole strength of each part

Since the pole strength is proportional to the product of the magnet's length, width and thickness, we can express the pole strength of a single part (m') as: \(m' \propto LW\) Where L and W are the length and width of a single part respectively. Now, let's substitute the dimensions of the smaller magnets: \(m' \propto \frac{L}{2} \times \frac{W}{2}\) \(m' \propto \frac{LW}{4}\) Since the proportionality constant is the same for both the original magnet and the smaller pieces, we can write: \(\frac{m'}{m} = \frac{\frac{LW}{4}}{LW}\) By simplifying the equation, we get: \(m' = \frac{m}{4}\)
04

Choose the correct answer

Comparing our result with the given options, we can see that the pole strength of each part is: (a) \(\frac{m}{4}\) This is in alignment with our calculated result in Step 3. Therefore, the correct answer is (a). Each part of the divided magnet will have a pole strength of \(\frac{m}{4}\).

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Most popular questions from this chapter

The angles of dip at two places are \(30^{\circ}\) and \(45^{\circ}\). The ratio of horizontal components of earth's magnetic field at the two places will be (a) \(\sqrt{3}: \sqrt{2}\) (b) \(1: \sqrt{2}\) (c) \(1: 2\) (d) \(1: \sqrt{3}\)

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