Two small spheres spread 10 cm apart have equal but opposite charge. If the magnitude of the force between them is 2.5 x 10^-10 N
(a)Calculate the charge on each sphere.
(b)Calculate the electric field intensity at the mid-point.
(c)Calculate the electric potential at the mid-point.
(d) How many excess electrons must be present on each sphere.
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Expert's answer
2019-06-25T09:16:54-0400
a) According to Coulomb's law for two equal charges:
F=4πϵ01⋅r2q2,
q=2rπϵ0F=1.667⋅10−11 C.
b) The field at the midpoint is a sum of fields of two charges. Since they have opposite signs, in the middle the field is twice as the field of a single charge (because the field is a vector quantity):
E=2⋅4πϵ01⋅(r/2)2q=119.86 V/m.
c) The electric potential is 0 in the middle since the two charges are equal but opposite:
V=4πϵ01⋅r/2q−4πϵ01⋅r/2q=0.
d) It's easy to calculate by dividing the total charge of a sphere by the charge of an electron:
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