In the figure below, positive charge q = 7.81 pC is spread uniformly along a thi

Question

In the figure below, positive charge q = 7.81 pC is spread uniformly along a thin nonconducting rod of length L = 18.0 cm.

What is the magnitude of the electric field produced at point P, at distance R = 6.00 cm from the rod along its perpendicular bisector?

figure: http://www.webassign.net/hrw/22-45.gif

In the figure below, positive charge q = 7.81 pC is spread uniformly along a thin nonconducting rod of length L = 18.0 cm. What is the magnitude of the electric field produced at point P, at distance R = 6.00 cm from the rod along its perpendicular bisector?

Explanation / Answer

Charge per unit length
? = q/L = 7.81 x10^-12 / (18x10^-2)= 4.33 x 10^-11 C/m

Electric field at point P is given by formula,

E = 2k?sin(?)/y, where
k=9x10^9 Nm^2C^-2

y=R = 6.00 cm= 6x10^-2 m

sin(?) = (L/2)/sqrt(L^2/4 + y^2) = L/sqrt(L^2 + 4y^2) = 18/sqrt(12^2+6^2)=1.34

So putting these values in above equation,
E=2x9x10^9x6.51 x 10^-11x1.34/(6x10^-2)= 26.16 N/C

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