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a ball with a mass of 100g is tied to a ceiling on a 1m cord and is charged with a positive charge of 3*10^16 c, what angle will the cord lift to if it is placed next to an infinite board charged with a density of 5*10-6 c/m^2 (positive), the board is placed at a constant angle of 45 degrees to the floor.

first i broke up the vectors of powers working on the ball,

Y+
Fcos45
Tcos(alpha)
--------
Y-
mg
-------
X+
Fsin45
-------
X-
Tsin(alpha)
--------
now i compare

Fsin45=Tsin(alpha)
T=Fsin45/sin(alpha)

mg=Fcos45+Tcos(alpha)
=Fcos45+(Fsin45/sin(alpha))*cos(alpha)
=Fcos45+Fsin45*cot(alpha)

cot(alpha)=(mg-Fcos45)/Fsin45

F=E*q
E=2(pi)(density)(k)
F=2(pi)(density)(k)(q)
F=0.27(pi)

once i put al the values in, i get that alpha=32.37 degrees but the answer in my text book is not that, can you ssee where i have gone wrong