Explanation Let the centre of the semicircle be the origin of coordinates. The vector sum of the magnetic fields from the two long wire and from the semi circle is the magnetic field at the center of the semicircle. Right hand rule says that the fields from each of these point into the page so that the net magnetic field is the sum of the magnetic fields. Write the expression for the magnetic field from the long straight wire. B → straight = μ 0 I 4 π d l → × R ^ R 2 (I) Here, μ 0 is the permeability of free space, B straight is is the magnetic field of the long straight wire, d l → is the elemental length, R is the distance from the point. The magnetic field for the curved segment over the semicircle is given by, B → curve = μ 0 I 4 π ∫ 0 π r d l → × r ^ r 2 (II) Equation (I) can be rearranged as, B = ∫ μ 0 I 4 π d l → × R → R 3 (III) The position vector is given by, R → = − x i ^ − r j ^ (IV) Use equation (IV) in equation (III) and integrate from − ∞ to zero. B = μ 0 I 4 π ∫ − ∞ 0 d x i ^ × ( − x i ^ − r j ^ ) ( x 2 + r 2 ) 3 / 2 = − μ 0 I r 4 π k

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ISBN: 9780133899634

Author: GIANCOLI

Publisher: PEARSON CO

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

Question

Chapter 28, Problem 72GP

To determine

The value of B at the centre of the 4.0 cm radius semicircle in Fig.28.61.

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Chapter 28, Problem 71GP

Chapter 28, Problem 73GP

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Chapter 28 Solutions

EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST

Ch. 28.1 - In Example 2510 we saw that a typical lightning...Ch. 28.1 - Suppose both I1 and I2 point into the page in Fig....Ch. 28.4 - Prob. 1CE Ch. 28 - The magnetic field due to current in wires in your...Ch. 28 - Compare and contrast the magnetic field due to a...Ch. 28 - Two insulated long wires carrying equal currents I...Ch. 28 - Prob. 4Q Ch. 28 - A horizontal current-carrying wire, free to move...Ch. 28 - (a) Write Ampres law for a path that surrounds...Ch. 28 - Suppose the cylindrical conductor of Fig. 2811a...

Ch. 28 - Explain why a field such as that shown in Fig....Ch. 28 - Prob. 9Q Ch. 28 - Use the Biot-Savart law to show that the field of...Ch. 28 - Prob. 11Q Ch. 28 - Why does twisting the lead-in wires to electrical...Ch. 28 - Compare the Biot-Savart law with Coulombs law....Ch. 28 - How might you define or determine the magnetic...Ch. 28 - How might you measure the magnetic dipole moment...Ch. 28 - A type of magnetic switch similar to a solenoid is...Ch. 28 - A heavy magnet attracts, from rest, a heavy block...Ch. 28 - Will a magnet attract any metallic object, such as...Ch. 28 - An unmagnetized nail will not attract an...Ch. 28 - Prob. 20Q Ch. 28 - Prob. 21Q Ch. 28 - Prob. 22Q Ch. 28 - Prob. 23Q Ch. 28 - Two iron bars attract each other no matter which...Ch. 28 - Describe the magnetization curve for (a) a...Ch. 28 - Prob. 26Q Ch. 28 - (I) Jumper cables used to start a stalled vehicle...Ch. 28 - (I) If an electric wire is allowed to produce a...Ch. 28 - Prob. 3P Ch. 28 - Prob. 4P Ch. 28 - Prob. 5P Ch. 28 - (II) An experiment on the Earths magnetic field is...Ch. 28 - Prob. 7P Ch. 28 - At the location of the compass, the magnetic field...Ch. 28 - (II) A long horizontal wire carries 24.0 A of...Ch. 28 - (II) A straight stream of protons passes a given...Ch. 28 - (II) Determine the magnetic field midway between...Ch. 28 - (II) Two straight parallel wires are separated by...Ch. 28 - (II) Two long straight wires each carry a current...Ch. 28 - (II) A long pair of insulated wires serves to...Ch. 28 - (II) A third wire is placed in the plane of the...Ch. 28 - (II) A power line carries a current of 95 A west...Ch. 28 - (II) A compass needle points 28 E of N outdoors....Ch. 28 - Prob. 18P Ch. 28 - (II) Let two long parallel wires, a distance d...Ch. 28 - (II) Repeat Problem 19 if the wire at x = 0...Ch. 28 - (II) Two long wires are oriented so that they are...Ch. 28 - (II) Two long parallel wires 8.20 cm apart carry...Ch. 28 - (III) A very long flat conducting strip of width d...Ch. 28 - (III) A triangular loop of side length a carries a...Ch. 28 - Prob. 25P Ch. 28 - Prob. 26P Ch. 28 - (I) A 2.5-mm-diameter copper wire carries a 33-A...Ch. 28 - (II) A toroid (Fig. 2817) has a 50.0-cm inner...Ch. 28 - Prob. 29P Ch. 28 - (II) (a) Use Eq. 281, and the vector nature of B,...Ch. 28 - (II) A coaxial cable consists of a solid inner...Ch. 28 - (III) Suppose the current in the coaxial cable of...Ch. 28 - Prob. 33P Ch. 28 - (II) A wire, in a plane, has the shape shown in...Ch. 28 - (II) A circular conducting ring of radius R is...Ch. 28 - (II) A small loop of wire of radius 1.8 cm is...Ch. 28 - Prob. 37P Ch. 28 - Prob. 38P Ch. 28 - Prob. 39P Ch. 28 - Prob. 40P Ch. 28 - Prob. 41P Ch. 28 - (III) Use the result of Problem 41 to find the...Ch. 28 - (III) A wire is bent into the shape of a regular...Ch. 28 - Prob. 44P Ch. 28 - Prob. 45P Ch. 28 - (III) A square loop of wire, of side d, carries a...Ch. 28 - (II) An iron atom has a magnetic dipole moment of...Ch. 28 - (I) The following are some values of B and B0 for...Ch. 28 - (I) A large thin toroid has 285 loops of wire per...Ch. 28 - (II) An iron-core solenoid is 38 cm long and 1.8...Ch. 28 - Three long parallel wires are 3.5 cm from one...Ch. 28 - Prob. 52GP Ch. 28 - Prob. 53GP Ch. 28 - Prob. 54GP Ch. 28 - Two long straight parallel wires are 15 cm apart....Ch. 28 - A rectangular loop of wire carries a 2.0-A current...Ch. 28 - Prob. 57GP Ch. 28 - A long horizontal wire carries a current of 48 A....Ch. 28 - A square loop of wire, of side d, carries a...Ch. 28 - Prob. 60GP Ch. 28 - Prob. 61GP Ch. 28 - For two long parallel wires separated by a...Ch. 28 - Near the Earths poles the magnetic field is about...Ch. 28 - A 175-g model airplane charged to 18.0 mC and...Ch. 28 - Suppose that an electromagnet uses a coil 2.0 m in...Ch. 28 - Four hour long straight parallel wires located at...Ch. 28 - Prob. 67GP Ch. 28 - A thin 12-cm-long solenoid has a total of 420...Ch. 28 - A 550-turn solenoid is 15 cm long. The current...Ch. 28 - Prob. 70GP Ch. 28 - Prob. 71GP Ch. 28 - Prob. 72GP Ch. 28 - Prob. 73GP Ch. 28 - Prob. 74GP Ch. 28 - (II) A circular current loop of radius 15 cm...Ch. 28 - (III) A set of Helmholtz coils (see Problem 61,...

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