A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of

Question

A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece.

A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. What is the length of one of these pieces? What is the location of the center of piece number 2? How much charge is on piece number 2? (Remember that the charge is negative.) Approximating piece 2 as a point charge, what is the electric field at location A due only to piece 2?

Explanation / Answer

a) 1.5/8 = 0.1875m

b) 2.5*0.1875 = (0,0.46875,0)m

c) -9*10^-8/8 = -1.125*10^-8 C

d) E = -8.98*10^9*1.125*10^-8/(0.7^2 + 0.46875^2) = -142.34 N/C

Ex = -142.34*0.7/0.842 = -118.33 N/C

Ey = -142.34*0.46875/0.842 = -79.24 N/C

Ez = 0

Hence (-118.33, -79.24, 0)

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