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mat-sln-asn-hwk14-spr02

# mat-sln-asn-hwk14-spr02 - Solution for Homework 14...

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Solution for Homework 14 Introduction to Magnetic Fields Solution to Homework Problem 14.1(Magnetic Field of Pith Ball) Problem: A pith ball is charged with an electrophorus to 1nC and shot along the x -axis at 100 m s in the + x direction. What is the magnitude of the magnetic field at (0 , 1cm , 0) when it reaches the origin? Select One of the Following: (a-Answer) 1 × 10 10 z (b) 2 × 10 10 Tˆy (c) 4 × 10 7 z (d) 3 × 10 11 z (e) 2 × 10 10 Tˆx Solution The magnetic field of a moving charge is vector B = μ 0 4 π qvectorv × ˆ r 10 r 2 10 where the vector vector r 10 points from the location of the charge to the location where the field is computed, q = 1nC is the charge, vectorv = 100 m s ˆx is the velocity. When the charge reaches the origin, vector r 10 = (0 , 1cm , 0) , r 10 = 1cm , and ˆ r 10 = ˆ y . Compute the cross product, vectorv × ˆ r 10 = 100 m s (ˆx × ˆy) = 100 m s ˆ z , where we use the right hand rule to solve the cross product. Substitute into the complete expression for vector B giving vector B = μ 0 4 π q r 2 10 ( vectorv × ˆ r 10 ) = parenleftbigg 4 π × 10 7 Tm A 4 π parenrightbiggparenleftbigg 1 × 10 9 C (0 . 01m) 2 parenrightbiggparenleftbigg 100 m s ˆ z parenrightbigg vector B = 1 × 10 10 z 2 point(s) : Magnitude 1 point(s) : Direction. Total Points for Problem: 3 Points Solution to Homework Problem 14.2(Right Handed Coordinate Systems) Problem: If the y axis points to the right of the page and the z axis points to the top of the page, what direction does the x axis point? Select One of the Following: (a) To the left of the page. (b) To the right of the page. (c) To the top of the page. (d) To the bottom of the page.

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mat-sln-asn-hwk14-spr02 - Solution for Homework 14...

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