Answer:
q = 1.04×10^-9C
Explanation:
The force on a charge orbiting at the center of the sphere (Fc) is must be equal to the electrostatic force acting on the charge.(Fq)
Fc = Fq
The force that causes a body to bev attracted towards the center of the sphere is the centripetal force.
Centripetal force (Fc) = ma = mv²/r where m is the mass of the body
v is the speed
r is the velocity
The electrostatic force acting on the body is derived according to the Coulomb's law of electrostatic attraction.
Fq = kqe/r²
Where k is the constant
e is the electron orbiting outside the sphere
r is the distance between the charge and the electron
Since fc=fq,
mv²/r = kqe/r²
Making the charge the subject of the formula we have;
mv²r = kqe
q = mv²r/ke
Given the mass of the charge =
8.84×10^-12kg
v = 3.0×10^5
r = 1.0cm = 0.01m
k = 1/4Π£o = 1/4Π×1.67×10^-27
k = 4.77×10^-27
e = 1.6×10^-19C
Substituting the values in the formula given,
q = 8.84×10^-12×(3.0×10^5)²(0.01)/(4.77×10^-27)×1.6×10^-19
q = 1.04×10^-9C
The sphere's charge is 1.04×10^-9
