Consider a point charge C above the mid-point of a line segment of length 2 L,...

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Consider a point charge C₁ above the mid-point of a line segment of length 2 L, which has total charge C2. The minimum distance between the point and the line is h and the line is assumed to be uniformly charged. (a) (b) Using Coulomb's inverse-square law, f = k192, and your math skills, show that the electrostatic force acting on the point from the line segment is F = kC₁ C₂ h√L²+h² 1 X You may use the result that f dx = (x²+y²)z y²√x²+y² What if the line is infinitely long and the charge density remains constant? In other words, what happens to your expression in (a) as L→∞? (Hint: If charge densitv remains constant then C2 will be proportional to L) (c) In the case of (b), i.e., if the line is infinitely long, assume that the point charge weighs 0.1 g, and C₁ = 1 µC. Work out the charge density the line must have in order for the particle to be held still at a distance of 30 cm above the line. (Hint: Coulomb's constant is k = 8.988x10⁹ Nm²/C²) Consider a point charge C₁ above the mid-point of a line segment of length 2 L, which has total charge C2. The minimum distance between the point and the line is h and the line is assumed to be uniformly charged. (a) (b) Using Coulomb's inverse-square law, f = k192, and your math skills, show that the electrostatic force acting on the point from the line segment is F = kC₁ C₂ h√L²+h² 1 X You may use the result that f dx = (x²+y²)z y²√x²+y² What if the line is infinitely long and the charge density remains constant? In other words, what happens to your expression in (a) as L→∞? (Hint: If charge densitv remains constant then C2 will be proportional to L) (c) In the case of (b), i.e., if the line is infinitely long, assume that the point charge weighs 0.1 g, and C₁ = 1 µC. Work out the charge density the line must have in order for the particle to be held still at a distance of 30 cm above the line. (Hint: Coulomb's constant is k = 8.988x10⁹ Nm²/C²)

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a To calculate the electrostatic force acting on the point charge from the line segment we need to c... View the full answer