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# 329sp08hw2 - ECE 329 Homework 2 Due 5PM 1 In this problem...

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ECE 329 Homework 2 Due: Jan 28, 2008, 5PM 1. In this problem we will compare the magnitudes of electrical force q E and magnetic force q v × B on a moving test charge q due to fields E and B produced by another charge Q at some distance r . a) Let E be the static Coulomb field of Q with magnitude Q 4 πǫ o r 2 . Also let B the magnetic field calculated using Biot-Savart law with a maximum magnitude μ o I | d l | 4 πr 2 where for I | d l | we can use QV s , where V s denotes the speed of charge Q when it is moving to produce B . Denoting the speed of the test charge as v q , show that the magnetic force on q can be as strong as the electric force only in the limit when the product of v q and V s approaches c 2 1 μ o ǫ o , where c 3 × 10 8 m/s. Hint: what is the expression for the largest possible magnitude for the ratio of q v q × B and q E ? b) The result of part (a) shows that magnetic force is typically much weaker than the electro- static force (when elementary sources are considered one at a time). Why then are magnetic effects observed in everyday life (e.g., pull and push of refrigerator magnets) often stronger than

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329sp08hw2 - ECE 329 Homework 2 Due 5PM 1 In this problem...

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