Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33×10-21N?

Short Answer

Expert verified

The number of excess electron on each sphere is 760 electrons .

Step by step solution

01

Step 1: Concept of Coulomb’s Law

According to the Coulomb’s law, the force between two charges spaced at a distance is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.

Mathematically,

F=k|q1q2|r2 ….. (1)

Here, F is the force, q1 and q2are the charges, k is the Coulomb’s charge, and is the distance between two charges.

02

Determination of the number of excess electron on each sphere.

Consider the given data as below.

The repulsive force, F=3.33×10-21N

The Coulomb’s constant, k=9×109N·m2/C2

The distance between charges, r=20cm=2.0m

Rewrite equation (1) as below.

F=kq2r2q=Fr2k

Substitute known values in the above equation, and you have

q=3.33×21-21N0.200m29×109N.m2/C2=1.217×10-16C

The charge of one electron is1.6×10-19C.

Thus, the number of electrons on each sphere is,

n=qe=1.217×10-16C1.6×10-19C/electron=760electron

Hence, there are 760 excess electrons on each sphere causing them to be negatively charged and repel each other.

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