Fly Fishing Gear

The electric field of uniformly charged rod?

A rod 12.0 cm long is uniformly charged and has a total charge of -21.0 µC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 30.0 cm from its center.

Edit:
The solution is revised. Earlier, the question was understood as 0.30 m from the end of the rod, whereas it is given to be 0.30 m from the center of the rod. The steps and answer have been corrected.

Consider a small length dx (meter) of the rod at a distance x (m) from the center of the rod nearest to the point.
Charge on it = - 21.0 x 10^-6 dx / (0.12) C.
Electric field at the point 30 cm from the center due to the charge on length dx of the rod
dE = [- 21.0 x 10^-6 / (0.12)] x 9 x 10^9 / (0.30 - x)^2 dx
Integrating between the limits, x = 0.06 m to x = 0.06 m,
E = ∫ - [21.0 x 10^-6 / (0.12)] x 9 x 10^9 / (0.30 - x)^2 dx ... [x = - 0.06 to x = 0.06]
= (1.575) x 10^6 ∫ dx / (0.30 - x)^2 ... [x = - 0.06 to x = 0.06]
= (1.575) x 10^6 * [1/(0.30 - x)] ... [x = - 0.06 to x = 0.06]
= (1.575) x 10^6 * [1/(0.24) - 1/(0.36)] N/C
= 2.1875 x 10^6 N/C.
The direction of the electric field is towards the rod along its length.

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