Question

Four questions. Please answer with all work shown so I can learn the methods. Thanks

(1)Two 2 cm-diameter disks spaced 2.187 mm apart form a parallel-plate capacitor. The electric field between the disks is 464,475.983 V/m.  An electron is launched from the negative plate. It strikes the positive plate at a speed of 29,140,951.095 m/s. What was the electron's speed as it left the negative plate?

(2)Two equally charged, 3.549 g spheres are placed with 2.925 cm between their centers. When released, each begins to accelerate at 320.079 m/s². What is the magnitude of the charge on each sphere?

(3)Object A, which has been charged to +12.39 nC, is at the origin. Object B, which has been charged to -25.5 nC, is at x=0 and y=2.07 cm.  What is the magnitude of the electric force on object A?

(4)A 5 cm spring is suspended with a mass of 3.8589 g attached to it which extends the spring by 1.5747 cm. The same spring is placed on a frictionless flat surface and charged beads are attached to each end of the spring. With the charged beads attached to the spring, the spring's extension is 0.0116 m. What are the charges of the beads?

Answer 1

1)

$F = qE = ma \Rightarrow a = \frac{q_eE}{m_e} = \frac{(1.602\times 10^{-19}C)(464,475.983 V / m)}{(9.10\times 10^{-31}kg)}$

now:

$a = \frac{v_f^2-v_0^2}{2d} \Rightarrow v_0^2 = v_f^2-a2d$

$v_0 = \sqrt{v_f^2-a2d} = \sqrt{29,140,951.095 m/s-(0.0817m/s^2)2(2.187 mm)}$