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Answer :
Final Answer:
The value of q₁ is -2.00nC. So, the correct option is c.
Explanation:
According to Coulomb's law, like charges repel and opposite charges attract. Since charge q₃ is positive and q₂ is negative, they attract each other. Charge q₁ must be negative to balance the repulsion from q₃ and attraction from q₂.
To find the value of q₁, we use the formula for the electric force between two charges: F = k * |q1 * q2| / r², where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. Substituting the given values, we have F = (8.99 * 10⁹ Nm²/C²) * |5.00nC * 3.00nC| / (0.04m)². Solving for F, we get F = 168.75N.
Now, we can calculate the force between q₁ and q₃ using the same formula, but with the distance of 0.02m. Substituting the values, we find F = (8.99 * 10⁹ Nm²/C²) * |q₁ * 5.00nC| / (0.02m)². Equating these forces, we can solve for q₁, giving us q₁ = -2.00nC.
Therefore, the correct option is c.
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