Electrostatics :: Problem 1

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Problem 1: Two unequal point charges repel each other with a force of 0.2N when they are 10cm apart. Find the force which each exerts on the other when they are:
(a) 1cm apart (b) 5cm apart.

Solution:

Step: 1 Overview

Coulomb's laws of electrostatic force says that when we place two charges at a distance of r meters, and magnitudes of charges are respectively q1 and q2, then force of attraction (in case of unlike charges) or repulsion (in case of like charges) will be equal to:

F=Kq₁q₂/r²

Step: 2 Calculation

Given:

F=0.2N, r=10cm=0.1m

Required:

F₁ (force at 1cm) and F₅ (force at 5cm)

According to given values:

F=Kq₁q₂/r²
0.2=Kq₁q₂/(0.1)²
Kq₁q₂=0.2(0.1)²
Kq₁q₂=0.2(0.01)
Kq₁q₂=0.002 --- (i)

We have of find F₁ and F₂:

F₁=Kq₁q₂/(0.01)²
according to equation (i) Kq₁q₂=0.002, so above equation becomes:
F₁=(0.002)/(0.0001)
F₁=20N (Ans)
Similiarly,
F₅=Kq₁q₂/(0.05)²
F₅=(0.002)/(0.0025)
F₅=0.8N (Ans)