solution to quiz1.tex 1. 1 → Φ E = 3 .0 × 10 6 Nm 2 /C 2 → Φ E = 0 hint: Φ E ≡ E A cos θ , where θ is the angle between the direction of the ﬁeld and the direction normal to the area. 2. stay the same hint: From Gauß’s theorem, the number of ﬁeld lines through a closed surface is proportional the enclosed charge, which is a constant for this problem. 3. 2 . 25 × 10-9 N/m hint: According to Hook’s law, | F | = κx where κ is the spring constant. On the other hand, F is just the Coulomb attraction between the two charges. 4. 5 × 10 5 N hint: The number of charges is n = 1 gram/m p where m p is the proton mass, so the resulting Coulomb force is F = k ( ne ) 2 / (2 R E ) 2 . 5. E a = kq/r 2 a , E b = 0, E c = kq/r 2 c hint: There will be a total charge of
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