Answer to Question #91101 in Electricity and Magnetism for Promise Omiponle

Question #91101
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.
1
Expert's answer
2019-06-25T09:16:54-0400

a) According to Coulomb's law for two equal charges:


F=14πϵ0q2r2,F=\frac{1}{4\pi\epsilon_0}\cdot\frac{q^2}{r^2},

q=2rπϵ0F=1.6671011 C.q=2r\sqrt{\pi\epsilon_0F}=1.667\cdot10^{-11}\text{ 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=214πϵ0q(r/2)2=119.86 V/m.E=2\cdot\frac{1}{4\pi\epsilon_0}\cdot\frac{q}{(r/2)^2}=119.86\text{ V/m}.

c) The electric potential is 0 in the middle since the two charges are equal but opposite:


V=14πϵ0qr/214πϵ0qr/2=0.V=\frac{1}{4\pi\epsilon_0}\cdot\frac{q}{r/2}-\frac{1}{4\pi\epsilon_0}\cdot\frac{q}{r/2}=0.

d) It's easy to calculate by dividing the total charge of a sphere by the charge of an electron:


N=qe=104050000.N=\frac{q}{e}=104050000.


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