Two charges repel each other with a force of 0.1 N when they are 5 cm apart. Find the forces between the same charges when they are 2 cm apart. Ans. (0.62 N)


Given:

Part-1
Coulomb's Force = F = 0.1 N
Distance between the charges= r  = 5 cm = 5100 = 0.05 m
Constant of proportionality = K = 9 ｘ 10⁹ Nm²C⁻²
Part-2
Distance between the charges= r  = 2 cm = 0.02 m

To Find:

The magnitude of the Coulomb's Force between the charges when they are (2cm = 0.02m) apart = F = ?

Solution: 

To find the Coulomb's force we also need to find first the magnitude of charges from the data of part-1 so,
According to Coulomb's Law

F = K q₁q₂r²

or

q₁q₂ = Fr²K

by putting the values

q₁q₂ = 0.1Nｘ(0.05)²9ｘ10⁹Nm²C⁻²

q₁q₂ = 0.1ｘ0.00259ｘ 10⁻⁹ C²

q₁q₂ = 0.00259ｘ 10⁻⁹ C²

q₁q₂ = 259 10⁻⁴ｘ 10⁻⁹ C²

q₁q₂ = 2.7777ｘ 10 ⁻¹³ C²

for the same charges and the data of part 2, we are again using Coulomb's law equation

F =  K q₁q₂r²

by putting values

F = 9 ｘ 10⁹ Nm²C⁻²  2.7777ｘ10⁻¹² C²(0.02)²

F = 9ｘ2.7770.004 10⁹ ｘ 10⁻¹³ N

F = 25ｘ10004 ｘ 10⁻⁴ N

F = 32.44 ｘ 1000ｘ 10⁻⁴ N

F = 6.25ｘ 10³ｘ 10⁻⁴ N

F = 6.25ｘ 10⁻¹ N

F = 0.625 N


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