Explanation Given data: Refer to the Figure P24.6 in the textbook. Formula used: Consider the expression for the magnetic field in a straight current carrying wire. B = μ 0 I 2 π r (1) Here, I is the current. r is the radius. μ 0 is the permeability of free space which has a constant value of 4 π × 10 − 7 T ⋅ m A . Calculation: Consider the magnetic field coming out of the page as positive and magnetic field going into the page as negative. For point 1, According to right hand thumb rule the magnetic field at point 1 is the magnetic field of upper wire subtracted with magnetic field of lower wire that is, B 1 = B upper − B lower (2) Here, B 1 is the magnetic field at 1. B upper is the magnetic field of upper wire. B lower is the magnetic field of lower wire. Substitute equation (1) in equation (2), B 1 = ( μ 0 I upper 2 π R upper ) − ( μ 0 I lower 2 π R lower ) (3) From the Figure, R lower = 4 cm + 2 cm = 6 cm Substitute 10 A for I upper , 10 A for I lower , 2 cm for R upper and 6 cm for R lower and 4 π × 10 − 7 T ⋅ m A for μ 0 in equation (3), B 1 = ( 4 π × 10 − 7 T ⋅ m A × 10 A 2 π × 2 cm ) − ( 4 π × 10 − 7 T ⋅ m A × 10 A 2 π × 6 cm ) = ( 4 π × 10 − 7 T ⋅ m A × 10 A 2 π × 2 × 10 − 2 m ) − ( 4 π × 10 − 7 T ⋅ m A × 10 A 2 π × 6 × 10 − 2 m ) = 1 × 10 − 4 T − 3.33 × 10 − 5 T = 6 .67 × 10 − 5 T As the magnetic field at the point 1 is positive so magnetic field is coming out of the page. For point 2, According to right hand thumb rule the magnetic field at point 2 is the magnetic field of upper wire added with magnetic field of lower wire in negative direction that is, B 2 = − ( B upper + B lower ) (4) Here, B 2 is the magnetic field at 2. Substitute equation (1) in equation (4), B 2 = − ( ( μ 0 I upper 2 π R upper ) + ( μ 0 I lower 2 π R lower ) ) (5) From the Figure, as the point 2 is in the center of the two wires so, R lower = 4 cm 2 = 2 cm And, R upper = 4 cm 2 = 2 cm Substitute 10 A for I upper , 10 A for I lower , 2 cm for R upper and 2 cm for R lower and 4 π × 10 − 7 T ⋅ m A for μ 0 in equation (5), B 2 = − ( ( 4 π × 10 − 7 T

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 24, Problem 6P

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The magnetic field strength and direction at point 1, 2, and 3 in FIGURE P24.6.

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Chapter 24, Problem 5P

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Chapter 24 Solutions

College Physics: A Strategic Approach (4th Edition)

Ch. 24 - In Figure Q24.1, suppose the magnet on the right...Ch. 24 - Prob. 2CQ Ch. 24 - When you are in the southern hemisphere, does a...Ch. 24 - If you were standing directly at the earths north...Ch. 24 - If you took a sample of magnetotactic bacteria...Ch. 24 - Green turtles use the earths magnetic field to...Ch. 24 - Prob. 7CQ Ch. 24 - Prob. 8CQ Ch. 24 - Prob. 9CQ Ch. 24 - As shown in Figure Q24.10, a uniform magnetic...

Ch. 24 - Prob. 11CQ Ch. 24 - An electron is moving in a circular orbit in a...Ch. 24 - Prob. 13CQ Ch. 24 - One long solenoid is placed inside another...Ch. 24 - Prob. 15CQ Ch. 24 - Prob. 16CQ Ch. 24 - Prob. 17CQ Ch. 24 - Prob. 18CQ Ch. 24 - An electron is moving near a long,...Ch. 24 - Two positive charges are moving in a uniform...Ch. 24 - Prob. 21CQ Ch. 24 - An electron and a proton are moving in circular...Ch. 24 - A proton moves in a region of uniform magnetic...Ch. 24 - Prob. 24CQ Ch. 24 - Prob. 25CQ Ch. 24 - A long wire and a square loop lie in the plane of...Ch. 24 - A solenoid carries a current that produces a field...Ch. 24 - Prob. 28CQ Ch. 24 - Prob. 29MCQ Ch. 24 - If a compass is placed above a current-carrying...Ch. 24 - Prob. 31MCQ Ch. 24 - Figure Q24.32 shows four particles moving to the...Ch. 24 - Prob. 33MCQ Ch. 24 - If all of the particles shown in Figure Q24.33 are...Ch. 24 - If two compasses are brought near enough to each...Ch. 24 - Table 24.1 notes that the magnetic field 10 cm...Ch. 24 - An investigator places a sample 1.0 cm from a wire...Ch. 24 - The magnetic field at the center of a...Ch. 24 - For a particular scientific experiment, it is...Ch. 24 - Prob. 5P Ch. 24 - Prob. 6P Ch. 24 - Prob. 7P Ch. 24 - Although the evidence is weak, there has been...Ch. 24 - Some consumer groups urge pregnant women not to...Ch. 24 - A long wire carrying a 5.0 A current perpendicular...Ch. 24 - Prob. 11P Ch. 24 - Prob. 12P Ch. 24 - A solenoid used to produce magnetic fields for...Ch. 24 - Two concentric current loops lie in the same...Ch. 24 - The magnetic field of the brain has been measured...Ch. 24 - Prob. 16P Ch. 24 - What is the magnetic field at the center of the...Ch. 24 - Experimental tests have shown that hammerhead...Ch. 24 - Prob. 19P Ch. 24 - Prob. 20P Ch. 24 - In the Bohr model of the hydrogen atom, the...Ch. 24 - A proton moves with a speed of 1.0 107 m/s in the...Ch. 24 - An electron moves with a speed of 1.0 107 m/s in...Ch. 24 - An electromagnetic flowmeter applies a magnetic...Ch. 24 - The aurora is caused when electrons and protons,...Ch. 24 - Problem 24.25 describes two particles that orbit...Ch. 24 - Prob. 27P Ch. 24 - Prob. 28P Ch. 24 - The microwaves in a microwave oven are produced in...Ch. 24 - A cyclotron is used to produce a beam of...Ch. 24 - A medical cyclotron used in the production of...Ch. 24 - Prob. 32P Ch. 24 - Prob. 33P Ch. 24 - Prob. 34P Ch. 24 - Prob. 35P Ch. 24 - A uniform 2.5 T magnetic field points to the...Ch. 24 - Prob. 37P Ch. 24 - A current loop in a motor has an area of 0.85 cm2....Ch. 24 - A square current loop 5.0 cm on each side carries...Ch. 24 - People have proposed driving motors with the...Ch. 24 - Prob. 41P Ch. 24 - Prob. 42P Ch. 24 - A solenoid is near a piece of iron, as shown in...Ch. 24 - The right edge of the circuit in Figure P24.44...Ch. 24 - Prob. 45GP Ch. 24 - An electron travels with speed 1.0 107 m/s...Ch. 24 - Prob. 47GP Ch. 24 - Prob. 48GP Ch. 24 - Irrigation channels that require regular flow...Ch. 24 - Typical blood velocities in the coronary arteries...Ch. 24 - Prob. 51GP Ch. 24 - Bats are capable of navigating using the earths...Ch. 24 - At the equator, the earths field is essentially...Ch. 24 - Prob. 55GP Ch. 24 - A 1.0-m-long, 1.0-mm-diaraeter copper wire carries...Ch. 24 - An insulated copper wire is wrapped around an iron...Ch. 24 - Prob. 58GP Ch. 24 - Assuming the particle in Figure P24.59 is...Ch. 24 - How does the kinetic energy of the particle in...Ch. 24 - Prob. 61MSPP Ch. 24 - Next, a particle with the same mass and velocity...Ch. 24 - What is the direction of the magnetic force on a...Ch. 24 - What is the magnitude of the force on this ion? A....Ch. 24 - What magnitude electric field is necessary to...Ch. 24 - The electric field produces a potential...Ch. 24 - In the spectrometer shown in Figure P24.67, do the...Ch. 24 - The moving ions can be thought of as a current...Ch. 24 - Why is it important that the ions have a known...Ch. 24 - A mass spectrometer similar to the one in Figure...

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