A point charge of mass 0.210 kg, and net charge +0.340*10^-6C, hangs at rest at

Question

A point charge of mass 0.210 kg, and net charge +0.340*10^-6C, hangs at rest at the end of an insulating string above a large sheet of charge. The horizontal sheet of uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the string is measured to be 5.67 N. Calculate the magnitude and direction of the electric field due to the sheet of charge.

I am not entirely sure how to do this, but this is my guess..could someone tell me if I am doing this right?

Ft-mg-Fe=0
Fe=Ft-mg
Fc=3.612 N

E=F/q
E=3.612/.340E-6
E=10623529.4 N/C <-------------- Is this right?

How do I determine the direction of the field?

Explanation / Answer

The mass of the charge m = 0.21kg the charge q = 0.34*10^-6 C the tension in the string T = 5.67N The solution what you done is correct, when there is tension in the string, then the charge should be attrated towards sheet, it means that the electric field should be pointed downwards. From Newton's law    FT - mg - F = 0 then    F = FT - mg       = (5.67N) - (0.21 kg)(9.8 m/s^2)       = 5.67 -   2.058 = 3.612 N Now F = qE therefore the electric field    E = F/q = 3.612 /0 .34*10^-6       = 10.6*10^6 N and the direction is towards downwards.   

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