Electricity and Magnetism

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?

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.

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.

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.

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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