Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 20, Problem 40P
To determine

The magnitude and direction of the current in the wire.

Expert Solution & Answer
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Answer to Problem 40P

The current in the wire is 19.4 A facing down.

Explanation of Solution

Given:

A compass needle changes its direction from 23° E of N to 55°E of N from the vertical wire, when placed 12 cm east of wire.

Earth’s magnetic field is 0.5×104 T horizontally.

Formula used:

According to the law of sines,

  FAsinθA=FBsinθB

Calculation:

Considering, both the changes in the magnetic field around the wire is in the Earth’s magnetic field. According to the diagram below, compass needle is moving towards south direction. Thus, the net magnetic field due to wire must be towards south direction.

  Physics: Principles with Applications, Chapter 20, Problem 40P

Using the geometry of the figure, angles are θ=23° , θ+ϕ=55° , and β+θ+ϕ=180° .

So, ϕ=32° , and β=125° . Now, using the law of sines, magnetic field of the wire will be

  Bwiresinϕ=BEarthsinβBwire=BEarthsinϕsinβ=μ0I2πrI = BEarthsinϕsinβ2πrμ0I = (5×105T)sin320sin12502π(0.120 m)4π×107Tm/AI =19.4 A

Since the magnetic field in the wire is facing towards the south direction. Thus, current in the wire will be towards down.

Conclusion:

Thus, the current in the wire is 19.4 A facing down.

Chapter 20 Solutions

Physics: Principles with Applications

Ch. 20 - Prob. 11QCh. 20 - Prob. 12QCh. 20 - 13. Explain why a strong magnet held near a CRT...Ch. 20 - Prob. 14QCh. 20 - Prob. 15QCh. 20 - Prob. 16QCh. 20 - Prob. 17QCh. 20 - If a moving charged particle is deflected sideways...Ch. 20 - Prob. 19QCh. 20 - Prob. 20QCh. 20 - Prob. 21QCh. 20 - Prob. 22QCh. 20 - Prob. 23QCh. 20 - Why will either pole of a magnet attract an...Ch. 20 - Prob. 25QCh. 20 - Prob. 26QCh. 20 - Prob. 27QCh. 20 - Prob. 28QCh. 20 - Prob. 29QCh. 20 - Prob. 30QCh. 20 - Prob. 31QCh. 20 - Prob. 1PCh. 20 - Prob. 2PCh. 20 - A 240-m length of wire stretches between two...Ch. 20 - Prob. 4PCh. 20 - Prob. 5PCh. 20 - Prob. 6PCh. 20 - Prob. 7PCh. 20 - Prob. 8PCh. 20 - Prob. 9PCh. 20 - Prob. 10PCh. 20 - Prob. 11PCh. 20 - Find the direction of the force on a negative...Ch. 20 - Prob. 13PCh. 20 - Prob. 14PCh. 20 - Prob. 15PCh. 20 - Prob. 16PCh. 20 - Prob. 17PCh. 20 - Prob. 18PCh. 20 - Prob. 19PCh. 20 - Prob. 20PCh. 20 - Prob. 21PCh. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - Prob. 26PCh. 20 - Prob. 27PCh. 20 - Prob. 28PCh. 20 - Prob. 29PCh. 20 - Prob. 30PCh. 20 - Prob. 31PCh. 20 - Prob. 32PCh. 20 - Prob. 33PCh. 20 - Prob. 34PCh. 20 - Prob. 35PCh. 20 - Prob. 36PCh. 20 - Prob. 37PCh. 20 - Prob. 38PCh. 20 - Prob. 39PCh. 20 - Prob. 40PCh. 20 - Prob. 41PCh. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - Prob. 44PCh. 20 - Prob. 45PCh. 20 - Prob. 46PCh. 20 - Prob. 47PCh. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Prob. 50PCh. 20 - Prob. 51PCh. 20 - Prob. 52PCh. 20 - Prob. 53PCh. 20 - A circular coil 12.0 cm in diameter and containing...Ch. 20 - Prob. 55PCh. 20 - Prob. 56PCh. 20 - Prob. 57PCh. 20 - Prob. 58PCh. 20 - Prob. 59PCh. 20 - Prob. 60PCh. 20 - Prob. 61PCh. 20 - Prob. 62PCh. 20 - Prob. 63PCh. 20 - Prob. 64PCh. 20 - Prob. 65PCh. 20 - Prob. 66PCh. 20 - Prob. 67GPCh. 20 - Prob. 68GPCh. 20 - Prob. 69GPCh. 20 - Prob. 70GPCh. 20 - Prob. 71GPCh. 20 - Prob. 72GPCh. 20 - Prob. 73GPCh. 20 - Prob. 74GPCh. 20 - Prob. 75GPCh. 20 - Prob. 76GPCh. 20 - Prob. 77GPCh. 20 - Prob. 78GPCh. 20 - Prob. 79GPCh. 20 - Prob. 80GPCh. 20 - Prob. 81GPCh. 20 - Prob. 82GPCh. 20 - Prob. 83GPCh. 20 - Prob. 84GPCh. 20 - Prob. 85GPCh. 20 - Prob. 86GPCh. 20 - Prob. 87GP

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