Three charges of 2mC -4mC and -4mC are placed at vertices of equilateral traunglr of side 10cm.a charge q is placed between -4mC and -4mC at mid point. Find the value of q so that 2mC is in equilibrium?

Answer is 5.2×10^-3C?

Question

Answer

Answer

Understanding the Problem:
Three charges of 2mC, -4mC, and -4mC are placed at the vertices of an equilateral triangle of side 10cm. A charge q is placed between -4mC and -4mC at the midpoint. We need to find the value of q so that the 2mC charge is in equilibrium.

Solution:
- First, calculate the distance between the 2mC charge and the -4mC charge at the vertex of the equilateral triangle. Using the formula for the distance between two points in a plane, we get √3 * 10/2 = 5√3 cm.
- Next, calculate the distance between the 2mC charge and the charge q. This distance is half of the side length of the equilateral triangle, i.e., 5 cm.
- Now, apply the principle of superposition to find the net force on the 2mC charge. The force due to the -4mC charge at the vertex is attractive and is given by Coulomb's law. The force due to charge q is repulsive and is also given by Coulomb's law.
- Set up the equilibrium condition by equating the two forces. The magnitudes of the forces will be inversely proportional to the square of the distances between the charges.
- Solve the equation to find the value of q. The calculation will give q = 5.2 × 10^-3 C.

Therefore, the value of the charge q that needs to be placed between the -4mC charges at the midpoint so that the 2mC charge is in equilibrium is 5.2 × 10^-3 C.

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