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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.

# Electrostatics

As shown in the above figure, the point charges $$q_A = 4 \text{ C}$$ and $$q_B$$ produce potential $$V$$ at the point $$X,$$ which is away from $$q_A$$ by a distance of $$d$$ and away from $$q_B$$ by a distance of $$2d.$$ If the point charge $$q_C$$ is away from $$X$$ by a distance of $$d$$ and the total potential at $$X$$ is $$-3V,$$ what is the sum of the point charges $$q_A,$$ $$q_B$$ and $$q_C?$$

There are two charged metal spheres, as shown in the above figure. The sphere $$A$$ with radius $$r_1 =16 \text{ cm}$$ is charged with charge $$Q_1 =32 \text{ C} ,$$ and the sphere $$B$$ with radius $$r_2 =8 \text{ cm}$$ is charged with charge $$Q_2 = 4 \text{ C}.$$ If the two spheres touch each other, what is the final charge of the sphere $$A?$$

Two identical, equally charged metal spheres $$A$$ and $$B$$ with radius $$3 \text{ m}$$ repel each other with a force of $$F_{AB} = 5 \times 10^{-5} \text{ N}.$$ A third identical, uncharged sphere $$C$$ touches $$A,$$ and then is placed at the midpoint of $$A$$ and $$B.$$ Determine the magnitude of net electrostatic force on $$C?$$

Three positively charged particles lie on a straight line. Their charges are $$q_1= 4 \text{ C}, q_2 =5 \text{ C}$$ and $$q_3=16 \text{ C},$$ with positions $$x_1 = 0,$$ $$x_2$$ and $$x_3 = r = 24 \text{ m}$$. The equilibrium point is placed between $$q_1$$ and $$q_3.$$

When $$q_1$$ and $$q_3$$ are fixed, and $$q_2$$ is movable, find the equilibrium point for $$q_2.$$

As shown in the above diagram, there are three electrically neutral metal spheres: metal sphere $$A$$ with radius $$r_A=4 \text{ cm},$$ metal sphere $$B$$ with radius $$r_B = 2 \text{ cm}$$ which is positively charged with charge $$q_B = 6.0 \text{ C} ,$$ and metal sphere $$C$$ with radius $$r_C = 6 \text{ cm}$$ which is negatively charged with charge $$q_C = -10.0 \text{ C}.$$ If $$B$$ touches $$A$$ and then touches $$C,$$ what is the final charge of sphere $$B?$$

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