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Electric Fields

Electric fields describe the interaction of stationary charged matter. They underlie the working of diverse technology from atom smashers to the poor cell reception you're getting right now.

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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