A small, charged insulating sphere with a mass of 2 grams is attached to a 10 co

Question

A small, charged insulating sphere with a mass of 2 grams is attached to a 10 com thread that is fixed in the middle of a very large vertical wall (an insulator). The wall has a uniform charge density of +10 µC/m2. The electrostatic force pushes the sphere away from the wall such that the angle that the thread makes with respect to the wall is 10°. (A) Draw a diagram of the situation, labeling your known and unknown parameters, and include a force diagram. (B) What is the charge on the sphere?

Explanation / Answer

let q is the charge on the sphere and T is the tension in the string

As the ball is in euilibrium net force acting on it must be zero.

Apply, Fnety = 0

T*cos(10) - m*g = 0

T*cos(10) = m*g ----(1)

Apply, Fnetx = 0

Fe - T*sin(10) = 0

T*sin(10) = Fe ----(2)

take equation(2)/equation(1)

tan(10) = Fe/(m*g)

m*g*tan(10) = Fe

m*g*tan(10) = q*E

m*g*tan(10) = q*sigma/(2*epsilon)

==> q = m*g*tan(10)*2*epsilon/sigma

= 2*10^-3*9.8*tan(10)*2*8.854*10^-12/(10*10^-6)

= 6.12*10^-9 C or 6.12 nC

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