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Junior Executive (AO) Official Paper 1: Held on Sep 2016

Option 4 : -9 q_{1}

CT 3: Building Materials

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10 Questions
20 Marks
12 Mins

__Coulomb’s law__**:**

When two charged particles of charges q1 and q2 are separated by a distance r from each other then the electrostatic force between them is directly proportional to the multiplication of charges of two particles and inversely proportional to the square of the distance between them.

Force (F) ∝ q1 × q2

\(F \propto \frac{1}{{{r^2}}}\)

\(F = K\frac{{{q_1} \times {q_2}}}{{{r^2}}}\)

Where K is a constant = 9 × 109 Nm2/C2

__Calculation__:

The given situation can be visualized as shown:

The force on Q because of q_{1} will be:

\({F_{Q{q_1}}} = \frac{{kQ{q_1}}}{{{a^2}}}\)

Similarly, the force on Q because of q_{2} will be:

\({F_{Q{q_2}}} = \frac{{kQ{q_2}}}{{{{\left( {3a} \right)}^2}}}\)

For the net charge at Q to be zero, we write:

\(\frac{{kQ{q_1}}}{{{a^2}}} + \frac{{kQ{q_2}}}{{9{a^2}}} = 0\)

\(\frac{{{q_1}}}{{{a^2}}} = \frac{{ - {q_2}}}{{9{a^2}}}\)

**q _{2} = -9q_{1}**