A uniformly-charged rod lies along the x axis from the origin to (x, y) = (+ 3,

Question

A uniformly-charged rod lies along the x axis from the origin to (x, y) = (+ 3, 0) cm. The total charge on the rod is -8 mu C. (a) What is the magnitude and direction of the electric field at (x, y) = (- 3, 0) cm.? Is this magnitude larger or smaller than the electric field that you would calculate from a point charge of -8 mu C at the origin? (b) What is the magnitude and direction of the electric field at (x, y) = (0, + 3) cm? Is this magnitude larger or smaller than the electric field that you would calculate from a point charge of - 8 mu C at the origin ?

Explanation / Answer

a] E = k lambda*[ 1/b - 1/(L+b)]

= 9e9*8e-6/0.03* [ 1/0.03 - 1/(0.03+0.03)]

= 4*10^7 N/C

direction = +x axis

smaller than point charge

b] Ex = 9e9*(8e-6/0.03)/0.03* [ sin 0 degree + sin 45 degree ]

= 5.66*10^7 N/C

Ey = 9e9*(8e-6/0.03)* [1/( 0.03 sqrt 2) - 1/0.03 ]

= 2.34*10^-7

Enet = sqrt(5.66^2+2.34^2) = 6.12*10^7

direction = 22.5 degree below x axis

smaller than point charge

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