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Fundamentals Of Physics
Found in: Page 716

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Short Answer

In Fig. 24-72, two particles of charges q1 and q2 are fixed to an x-axis. If a third particle, of charge +6.0μC, is brought from an infinite distance to point P, the three-particle system has the same electric potential energy as the original two-particle system. What is the charge ratio q1/q2?

The charge ratio q1/q2 is -1.66.

See the step by step solution

Step by Step Solution

Step 1: Given data:

Draw the given figure as below.

Here, q1 and q2 are fixed charges.

The charge, q3=+6.0μC=+6.0×10-6C

Step 2: Determining the concept:

Use the electric potential energy for the final three particle system,


If two like charges (two protons or two electrons) are brought towards each other, the potential energy of the system increases. If two unlike charges i.e. a proton and an electron are brought towards each other, the electric potential energy of the system decreases.


The electric potential is define by,


The bet potential is define by,


Where, U is electric potential energy, R is distance between the point charges, q is charge, ε0 is the permittivity of free space, and k is the Coulomb’s constant having a value

Step 3: Determining the charge ratio of 

The net potential energy is,


According to the given condition,


Hence, the charge ratio q1/q2 is -1.66.

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