Please Help me A thin rod of length 4 m, with charge -7 times 10-7 C uniformly d

Question

Please Help me

A thin rod of length 4 m, with charge -7 times 10-7 C uniformly distributed on its surface, lies on the x-axis as shown, with its center at the origin. You want to find the electric field at location A = m due to the charge on the entire rod. To do this, you divide the rod into 10 small pieces, which can be treated as point charges. At the observation location, draw an arrow representing delta E rightarrow the electric field due to piece number 8. What is the location of the center of piece number 8? Your answer should be a vector. Calculate the electric field at location A= m due only to piece number 8. Your answer must be a vector, with appropriate units. Explicitly show every step in your calculation.

Explanation / Answer

a)

b)

<1 , 0 , 0>

c)

E = k dq/r^2

dq is the charge on the piece #8 and equals to tenth of the -7 x 10^-7 C:

dq = (-7 x 10^-7)/10 = -7 x 10^-8 C

r is the distance from piece #8 to the point A:

r = sqrt((1 - (-0.2))y2 + (0 - (0.3))y2) = 1.2369 m

So:

E = k dq/r^2 = (9e9) * (7e-7)/(1.23698*1.2369) = 4117.59 N/C

Now we must find components of the electric field:

Ex = E * (x - xA)/r = 4117.59 * (1 - (-0.2))/1.2369 = 3994.75 = 3990 N/C

Ey = E * (y - yA)/r = 4117.59 * (0 - (0.3))/1.2369 = -998.688 = -999 N/C

Ez = 0 N/C

So

E = <3990 , -999 , 0> N/C

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