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The problem provided in the image is asking where a charge \( Q3 \) should be placed relative to charges \( Q1 \) and \( Q2 \) such that the net electrostatic force on \( Q3 \) is zero. The charges are given as \( Q1 = -16 \mu C \), \( Q2 = +36 \mu C \), and \( Q3 = 10 \mu C \). The distance \( R \) between \( Q1 \) and \( Q2 \) is \( 9 \) cm.

### Solution:
To find the point where the net electrostatic force on \( Q3 \) is zero, we can use Coulomb's Law, which describes the force between two charges. The force \( F \) is given by:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.

To achieve zero net force on \( Q3 \), the force exerted by \( Q1 \) on \( Q3 \) must be equal in magnitude but opposite in direction to the force exerted by \( Q2 \) on \( Q3 \). Therefore, we must find a position \( x \) along the line connecting \( Q1 \) and \( Q2 \) such that:
\[ k \frac{|Q1 \cdot Q3|}{x^2} = k \frac{|Q2 \cdot Q3|}{(R-x)^2} \]

Substituting the given values:
\[ \frac{|-16 \cdot 10|}{x^2} = \frac{|36 \cdot 10|}{(9-x)^2} \]

Solving this equation will give the position \( x \) (in cm) from \( Q1 \) where \( Q3 \) should be placed. Let's calculate \( x \).The solutions for the position \( x \) where \( Q3 \) should be placed relative to \( Q1 \) are \(-18\) cm and \( \frac{18}{5} \) cm (or 3.6 cm). The negative value \(-18\) cm is not physically meaningful in this context as it implies a position outside the \( Q1 \) to \( Q2 \) interval. Thus, the meaningful position for \( Q3 \) to ensure a zero net force is 3.6 cm from \( Q1 \) towards \( Q2 \).

### Answer:
\( Q3 \) should be placed 3.6 cm from \( Q1 \) towards \( Q2 \) to have a net electrostatic force of zero.

Would you like more details on how this solution was derived, or do you have any other questions?

Here are some related questions you might find helpful:
1. What would be the electrostatic force experienced by \( Q3 \) if it was placed at the midpoint between \( Q1 \) and \( Q2 \)?
2. How would the solution change if \( Q3 \) had a different charge?
3. What is the importance of sign (positive or negative) in electrostatic force calculations?
4. How does the distance between charges affect the magnitude of the electrostatic force?
5. Can we place \( Q3 \) in any other position to achieve zero net force?

Tip: Remember, the principle of superposition in electrostatics allows us to analyze the effect of each charge separately before adding them vectorially.

Where should charge Q3 = 10μC be placed relative to Q1 = -16μC and Q2 = +36μC such that the net electrostatic force on Q3 is zero, given that the distance between Q1 and Q2 is 9 cm?

Learn how to determine the correct position to place a charge Q3 = 10μC relative to Q1 = -16μC and Q2 = +36μC such that the net electrostatic force on Q3 is zero. This physics problem involves using Coulomb's Law and solving a quadratic equation. Suitable for Grades 11-12.

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