1-Answer the following: a-A proton is held at a fixed position. An electron is p

Question

1-Answer the following:

a-A proton is held at a fixed position. An electron is placed 0.85 m away and released.Find the electron's speed when it's 2.0 mm from the proton.

b-Three capacitors are in series: C1 = 50 F , C2 = 70 F , and C3 = 90 F . The series combination is connected across a 48 V battery.

1-Compute the equivalent capacitance. 2-Find the charge on the capacitor C1 . 3-Compute the energy stored in the capacitor C1 . 4-Find the charge on the capacitor C2 .   5-Compute the energy stored in the capacitor C2 . 6-Find the charge on the capacitor C3 . 7-Compute the energy stored in the capacitor C3 .

Explanation / Answer

(A) Applyying energy conservation,

PEi + KEi = PEf + KEf

-(9x 10^9)(1.6 x 10^-19)^2 / (0.85) + 0 = -(9x 10^9)(1.6 x 10^-19)^2 / (0.002) + (9.109 x 10^-31)v^2 / 2

- 2.7106 x 10^-28 = -1.152 x 10^-25 + (9.109 x 10^-31 v^2) /2

v = 502.34 m/s ........Ans

b)

1. 1/Ceq = 1/C1 + 1/C2 + 1/C3

Ceq = 22 uF

2. charge on all three capacitor will be same.

Q = 22uF x 48 V = 1056 uC

3. U = Q^2 / 2C

= (1056 x 10^-6)^2 / (2 x 50 x 10^-6)

= 11.2 x 10^-3 J

4. Q2 = 1056 uC

5. U2 = Q2^2 / 2 C2 = 7.97 x 10^-3 J

6. Q3 = 1056 uC

7. U3 = 6.19 x 10^-3 J

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