Superposition of electric fields

         

Three point charges of strengths \( q_1 = 4.0 \times 10^{-6} \text{ C}, \) \( q_2 = 1. 0 \times 10^{-6} \text{ C} \) and \( Q = -4.0 \times 10^{-6} \text{ C}\) are fixed in a right triangle as shown above.

The distance between \( q_1 \) and \( Q \) is \( d_1 = 4.0 \text{ cm}, \) and the distance between \( q_2 \) and \( Q \) is \( d_2 = 3.0 \text{ cm}. \) What is the approximate electric field strength at location of charge \( Q \) due to the other two charges?

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Four point charges, each equal to \( q = 44 \ \mu \text{C}, \) are held at the corners of square \( ABCD\) of side length \( a= 80 \text{ cm} \) on the \(xy\)-plane. Find the magnitude and sign of a charge \( Q \) placed at the center of the square such that the system of charges is in equilibrium.

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Three point charges, each equal to \( q = 33 \ \mu \text{C}, \) are held at the corners of equilateral triangle \( ABC\) of side length \( a= 60 \text{ cm}\) on the \(xy\)-plane. Find the magnitude and sign of a charge \( Q \) placed at the center of the triangle such that the system of charges is in equilibrium.

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Two charges, each equal to \( -52 \ \mu \text{C}, \) are held a certain distance apart. A charge \( Q \) is placed exactly midway between them. Find the magnitude and sign of \( Q \) such that the system of the three charges is in equilibrium.

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Two points charges \( q_ 1 = 64 \ \mu \text{C} \) and \( q_2 = -9 \ \mu \text{C} \) are held on the \(x\)-axis. The point charge \( q_1 \) is at \( x = -50 \text{ cm} \) and \( q_2 \) is at the origin. Where on the \( x \)-axis should a third charge \( +Q \) be placed so that charge \( Q \) does not experience any net force?

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