Question

(12.) In nuclear fission, a nucleus splits roughly in half. (a) What is the potential 3.00 ✕ 10-14 m from a fragment that has 46 protons in it? 2.21e+06 V [My Answer 2.21e+6 V] (b) What is the potential energy in MeV of a similarly charged fragment at this distance? [My Answer 102 MeV]

(13) In one of the classic nuclear physics experiments at the beginning of the 20th century, an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction. If the energy of the doubly charged alpha nucleus was 5.03 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?[My Answer: 4.50e-14 m]

(14) Two charges q1 = −3.20 nC and q2 = +8.73 nC are at a distance of 1.98 μm from each other. q1 is fixed at its location while q2 is released from rest.
(a) What is the kinetic energy of the charge q2 when it is 0.340 μm from q1? [My Answer: 0.612 J
(b) The charge q2 has a mass m2 = 7.85 μg. What is its speed when it is 0.340 μm from q1?
[My Answer: 12500 m/s]

(15) A charge q1 = 1.52 uC is at a distance d = 1.23 m from a second charge q2 = -6.07 uC
(a) Find the electric potential at a point A between the two charges that is from q1. Note that the location A in
the diagram above is not to scale. [My Answer: -66500 V]
(b) Find a point between the two charges on the horizontal line where the electric potential is zero. (Enter your
answer as measured from q1.) [My Answer: 0.246 m]

(16) Four charges of equal magnitude q = 2.04 uC are situated (i.e., xy-plane) If d = 0.85m find electrical potential at location A due to the four charges [My Answer: -10800 V]

(17) In the diagram below, the two charges q1 = +q and q2 = −2q are fixed in place [use xy-plane to diagram program]. The distance between them is d = 5.35 m. Find the distance x of the point A on the horizontal line where the net electric potential due to the two charges is zero. [My Answer: 3.09 m]

(18) Three point charges q1, q2 and q3 are situated at three corners of a rectangle as shown in the diagram below. Here q1 = +5.00 uC q2 = -5.00 uC, q3 = +6.00 uC [Note side opposite q3 to q2 = 2.50 cm and side opposite q1 to 12 = 5.00 cm]
(a) What is the electric potential at the free corner where there is no charge?
[My Answer: 2.07e+06 V]
(b) What charge should be placed at the free corner for the electric potential at the center of the rectangle to be
zero? Include both magnitude and sign if applicable. [My Answer: -6 μC]

(19) Two point charges q₁ = +2.52 nC and q₂ = -2q₁ are located along the x-axis as shown in the diagram below. The
distance between the two charges is [use xy-plane]
(a) At what location A between the two charges on the x-axis will the electric potential be zero?
[My Answer: x = 1.03 m]

Answer 1

12. (A) q = 46 x 1.6 x 10^-19 C

q = 7.36 x 10^-18 C

V = k q / r = (9 x 10^9)(7.36 x 10^-18) / (3 x 10^-14)

V = 2.21 x 10^6 Volt  

(B) PE = q V = (7.36 x 10^-18)(2.21 x 10^6)

PE = 1.625 x 10^-11 J  

PE (in eV) = (1.625 x 10^-11)/(1.6 x 10^-19) = 101.6 x 10^6 eV  

PE = 101.6 MeV  

13. KEi = 5.03 MeV = 5.03 x 10^6 x 1.6 x 10^-19 J

KEi = 8.048 x 10^-13 J  

Applyng energy conservation,

PEi + KEi = PEf + KEF

0 + (8.048 x 10^-13) = k q1 q2 / r + 0

8.048 x 10^-13 = (9 x 10^9)(2 x 79)(1.6 x 10^-19)^2 / r

r = 4.52 x 10^-14 m