(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A straight, nonconducting plastic wire 8.00 cm long carries a charge density of 125 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop.

A) Find the magnitude and direction of the electric field this wire produces at a point 5.50 cm directly above its midpoint.

B) If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 5.50 cm directly above its center.

I have tried to figure it out, but I am having some issues.

2. Relevant equations

theta = r/(L/s)

E = Q/2πrεoL = ρL/2πrL = ρ/2πεor

3. The attempt at a solution

E = 125*10^-9/((2pi(0.055)8.85*10^-12 = 4.0871*10^4

Ey = Esin(theta)

theta = r/(L/s) = arctan(2*0.055)/0.08 =arctan(1.375) = 53.97 degrees

Ey= 4.0871*10^4 * sin53.97 degrees = 3.31*10^4

Alternatively, would I do arctan again for 53.57 degrees for 88.938 degrees? Then multiply it by 4.0871*10^4? The answer would be 4.086*10^4

Is this right?? Please help me.

b)

r= L/2pi = 0.08/2pi = 0.0126 m

d = square root(0.0126^2+0.055^2) = 0.0564 m

Ey = Esin(theta)

theta = arctan(0.055)/(0.0126m) = 77.1 degrees

Ey = PL/4piEor^2 = 125*10^-9 * 0.08 / 4pi(8.85*10^-12(0.055^2) = 2.97*10^4

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# Homework Help: Charge density for basic physics

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