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For the bar magnet of Prob. 6.9, make careful sketches of

Chapter 6, Problem 14P

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QUESTION:

Problem 14P

For the bar magnet of Prob. 6.9, make careful sketches of M, B, and H, assuming L is about 2a. Compare Prob. 4.17.

Reference 4.17

For the bar electret of Prob. 4.11, make three careful sketches: one of P, one of E, and one of D. Assume L is about 2a. [Hint: E lines terminate on charges; D lines terminate on free charges.]

Reference prob 4.11

A short cylinder, of radius a and length L, carries a “frozen-in” uniform polarization P, parallel to its axis. Find the bound charge, and sketch the electric field (i) for L ≫ a, (ii) for L ≫ a, and (iii) for L ≈ a. [This is known as a bar electret; it is the electrical analog to a bar magnet. In practice, only very special materials—barium titanate is the most “familiar” example—will hold a permanent electric polarization. That’s why you can’t buy electrets at the toy store.]

Reference 6.9

A short circular cylinder of radius a and length L carries a “frozen-in” uniform magnetizationMparallel to its axis. Find the bound current, and sketch the magnetic field of the cylinder. (Make three sketches: one for L ≫ a, one for L≫ a, and one for L ≈ a.) Compare this bar magnet with the bar electret of Prob. 4.11.

Questions & Answers

QUESTION:

Problem 14P

For the bar magnet of Prob. 6.9, make careful sketches of M, B, and H, assuming L is about 2a. Compare Prob. 4.17.

Reference 4.17

For the bar electret of Prob. 4.11, make three careful sketches: one of P, one of E, and one of D. Assume L is about 2a. [Hint: E lines terminate on charges; D lines terminate on free charges.]

Reference prob 4.11

A short cylinder, of radius a and length L, carries a “frozen-in” uniform polarization P, parallel to its axis. Find the bound charge, and sketch the electric field (i) for L ≫ a, (ii) for L ≫ a, and (iii) for L ≈ a. [This is known as a bar electret; it is the electrical analog to a bar magnet. In practice, only very special materials—barium titanate is the most “familiar” example—will hold a permanent electric polarization. That’s why you can’t buy electrets at the toy store.]

Reference 6.9

A short circular cylinder of radius a and length L carries a “frozen-in” uniform magnetizationMparallel to its axis. Find the bound current, and sketch the magnetic field of the cylinder. (Make three sketches: one for L ≫ a, one for L≫ a, and one for L ≈ a.) Compare this bar magnet with the bar electret of Prob. 4.11.

ANSWER:

Solution 14P

Step 1 of 4:

The field lines outside a bar magnet start from the North Pole and end at the South Pole. And inside, the lines start from the South Pole to the North Pole. The length of the bar magnet is two times its breadth (L = 2a). We are going to sketch the lines of M, B, and H.

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