Consider an infinitely thin charged rod of length L with uniform linear charge density å lying along the x-axis. The ends are at x = +L/2 and the center is at the origin. a. Calculate the electric field (magnitude and direction) for x > L/2. b. Calculate the force on a test particle with charge qo < 0 located at some position x> L/2. c. Show that the force on the test particle will simplify to Coulomb’s Law when it is sufficiently far away from the rod, i.e. when x >> L. Use Q= AL for the total charge on the rod.
Consider an infinitely thin charged rod of length L with uniform linear charge density å lying along the x-axis. The ends are at x = +L/2 and the center is at the origin. a. Calculate the electric field (magnitude and direction) for x > L/2. b. Calculate the force on a test particle with charge qo < 0 located at some position x> L/2. c. Show that the force on the test particle will simplify to Coulomb’s Law when it is sufficiently far away from the rod, i.e. when x >> L. Use Q= AL for the total charge on the rod.
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:Consider an infinitely thin charged rod of length L with uniform linear charge
density å lying along the x-axis. The ends are at x =±L/2 and the center is at the
origin.
a. Calculate the electric field (magnitude and direction) for x> L/2.
b. Calculate the force on a test particle with charge qo< 0 located at some
position x> L/2.
c. Show that the force on the test particle will simplify to Coulomb's Law
when it is sufficiently far away from the rod, i.e. when x >> L. Use Q=
AL for the total charge on the rod.
Expert Solution
Step 1
Part a:
The net electric field can be obtained by integrating over small fields due to charge dq on a line element dl at a distance l from the origin.
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