Explanation Draw the figure for magnetic field at center of equilateral triangle as. In the above equilateral triangle Δ A B C has equal length segment. Draw the perpendicular line A O on side B C , B N on side A C and C M on side A B . Each perpendicular line intersects to each other at point P . This point P called as centroid of the equilateral triangle. Consider triangle Δ A M P . tan 60 ° = A M M P 3 2 = L 2 x x = L 2 3 Here, x is the perpendicular length from centroid to the side of triangle and L is length of each side of triangle. Write the expression for magnetic moment at Centre as. B = μ 0 I 4 π x ( sin θ 1 + sin θ 2 ) (I) Here, I is current, μ 0 is permeability of free space, B is magnetic field, θ 1 is angle between A P and M P and θ 2 is the angle between P M and P B . Substitute L 2 3 for x and 60 ° for θ 1 and 60 ° for θ 2 in equation (I). B = μ 0 I 4 π L 2 3 ( sin 60 ° + sin 60 ° ) = 2 3 μ 0 I 4 π L ( 3 2 + 3 2 ) = ( 2 3 μ 0 I 4 π L ) 2 ( 3 2 ) = 6 μ 0 I 4 π L Write the expression for total magnetic field at centroid of the triangle for three sides as

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781337026345

Author: Katz

Publisher: Cengage

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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 30, Problem 25PQ

To determine

Find the magnetic field at center of equilateral triangle.

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Chapter 30 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 30.2 - Prob. 30.1CE Ch. 30.3 - Prob. 30.2CE Ch. 30.4 - Prob. 30.3CE Ch. 30.8 - Cosmic rays are high-energy charged particles...Ch. 30.9 - The Earths Van Allen belts (Fig. 30.34) are a...Ch. 30.10 - Prob. 30.6CE Ch. 30.10 - Prob. 30.7CE Ch. 30.12 - Prob. 30.8CE Ch. 30 - A yoga teacher tells her students to imagine their...Ch. 30 - Prob. 2PQ

Ch. 30 - Prob. 3PQ Ch. 30 - Prob. 4PQ Ch. 30 - Prob. 5PQ Ch. 30 - Copy Figure P30.6 and sketch the magnetic field...Ch. 30 - Prob. 7PQ Ch. 30 - Prob. 9PQ Ch. 30 - Figure P30.10 shows a circular current-carrying...Ch. 30 - Figure P30.11 shows three configurations of wires...Ch. 30 - Review A proton is accelerated from rest through a...Ch. 30 - An electron moves in a circle of radius r at...Ch. 30 - One common type of cosmic ray is a proton...Ch. 30 - Prob. 15PQ Ch. 30 - Prob. 16PQ Ch. 30 - Prob. 17PQ Ch. 30 - A Two long, straight, parallel wires are shown in...Ch. 30 - Prob. 19PQ Ch. 30 - Two long, straight, parallel wires carry current...Ch. 30 - Prob. 21PQ Ch. 30 - Two long, straight wires carry the same current as...Ch. 30 - Prob. 23PQ Ch. 30 - A wire is bent in the form of a square loop with...Ch. 30 - Prob. 25PQ Ch. 30 - A Derive an expression for the magnetic field...Ch. 30 - Prob. 27PQ Ch. 30 - Prob. 28PQ Ch. 30 - Prob. 29PQ Ch. 30 - Prob. 30PQ Ch. 30 - Prob. 31PQ Ch. 30 - Prob. 32PQ Ch. 30 - Prob. 33PQ Ch. 30 - Prob. 34PQ Ch. 30 - Normally a refrigerator is not magnetized. If you...Ch. 30 - Prob. 36PQ Ch. 30 - Prob. 37PQ Ch. 30 - The magnetic field in a region is given by...Ch. 30 - Prob. 39PQ Ch. 30 - Prob. 40PQ Ch. 30 - Prob. 41PQ Ch. 30 - The velocity vector of a singly charged helium ion...Ch. 30 - Prob. 43PQ Ch. 30 - Can you use a mass spectrometer to measure the...Ch. 30 - In a laboratory experiment, a beam of electrons is...Ch. 30 - Prob. 46PQ Ch. 30 - Prob. 47PQ Ch. 30 - Prob. 48PQ Ch. 30 - A proton and a helium nucleus (consisting of two...Ch. 30 - Two ions are accelerated from rest in a mass...Ch. 30 - Prob. 51PQ Ch. 30 - Prob. 52PQ Ch. 30 - A rectangular silver strip is 2.50 cm wide and...Ch. 30 - For both sketches in Figure P30.56, there is a...Ch. 30 - A 1.40-m section of a straight wire oriented along...Ch. 30 - Professor Edward Ney was the founder of infrared...Ch. 30 - Prob. 59PQ Ch. 30 - A wire with a current of I = 8.00 A directed along...Ch. 30 - Prob. 61PQ Ch. 30 - The triangular loop of wire shown in Figure P30.62...Ch. 30 - Prob. 63PQ Ch. 30 - Consider the wires described in Problem 63. Find...Ch. 30 - Prob. 65PQ Ch. 30 - Prob. 66PQ Ch. 30 - A Three parallel current-carrying wires are shown...Ch. 30 - Prob. 68PQ Ch. 30 - Prob. 69PQ Ch. 30 - Prob. 70PQ Ch. 30 - Prob. 71PQ Ch. 30 - Prob. 72PQ Ch. 30 - A circular coil 15.0 cm in radius and composed of...Ch. 30 - Prob. 74PQ Ch. 30 - Prob. 75PQ Ch. 30 - Prob. 76PQ Ch. 30 - Prob. 77PQ Ch. 30 - Two long, straight, current-carrying wires run...Ch. 30 - Prob. 79PQ Ch. 30 - Prob. 80PQ Ch. 30 - Prob. 81PQ Ch. 30 - Prob. 82PQ Ch. 30 - Two infinitely long current-carrying wires run...Ch. 30 - Prob. 84PQ Ch. 30 - Prob. 85PQ Ch. 30 - Prob. 86PQ Ch. 30 - A charged particle with charge q and velocity...Ch. 30 - Prob. 88PQ Ch. 30 - Prob. 89PQ Ch. 30 - A mass spectrometer (Fig. 30.40, page 956)...Ch. 30 - Three long, current-carrying wires are parallel to...Ch. 30 - Prob. 92PQ Ch. 30 - A current-carrying conductor PQ of mass m and...Ch. 30 - A proton enters a region with a uniform electric...

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