Question

A charged sphere of mass 0.62 kg and net charge 0.34 µC 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.
(a) In a free-body diagram, show the forces that act on the charged sphere.
(b) Calculate the magnitude and direction of the electric field due to the sheet of charge.

Answer 1

As per the given question,

charge on the sphere $(q)=0.34\mu C$

mass of the charged sphere $(m)=0.62kg$

Tension in the string $(T)=5.67N$

gravitational field $(g)=9.8 m/sec^2$

Let the electric field is E,

a)

b) $qE=mg+T$

$E=\dfrac{mg+T}{q}=\dfrac{0.62\times 9.8+5.67}{0.34\times 10^{-6}}$

$\Rightarrow E=34.54\times 10^6 N/c$ in upward direction.