PHYS 2212 Module 3 Self Assessment Practice Problems

Module 3 Self Assessment Practice Problems

3.1
How much work is needed to assemble an atomic nucleus containing three protons (such as Li) if we model it as an equilateral triangle of side 2.00 x 10-15 m with a proton at each vertex? Assume the protons started from very far away.
Answer:  3.5 x 10-13 J
3.2
(a) How much work would it take to push two protons very slowly (and at a constant speed) from a separation of 2.00 x 10-10 m (a typical atomic distance) to 3.00 x 10-15 m (a typical nuclear distance)?
(b) If the protons are both released from rest at the closer distance in part (a), how fast are they moving when they reach their original separation?
Answer:  (a) -7.7 x 10-14 J   (b) 9.6 x 106 m/s
3.3
To form a helium atom, an alpha particle that contains two protons and two neutrons is fixed at one location, and two electrons are brought in from far away, one at a time. The first electron is placed at 0.600 x 10-10 m from the alpha particle and held there while the second electron is brought to 0.600 x 10-10 m from the alpha particle on the other side from the first electron. 
(a) How much work is done in each step?
(b) What is the electrostatic energy of the alpha particle and two electrons in the final configuration?
Answer:  (a) W1 = 7.7 x 10-18 J, W2 = 5.8 x 10-18 J    (b) -13.5 x 10-18 J
3.4
An object with charge q = -5.00 x 10-9 C is placed in a region of uniform electric field and is released from rest at point A. After the charge has moved to point B, 0.500 m to the right, it has kinetic energy 3.00 x 10-7 J.
(a) If the electric potential at point A is +30.0 V, what is the electric potential at point B?
(b) What is the magnitude of the electric field?
(c) What is the direction of the electric field?
Answer:   (a) 90 V   (b) 120 V/m   (c) to the left
3.5
A small particle has charge -5.10 µC and mass 2.80 x 10-4 kg. It moves from point A, where the electric potential is VA = 270 V, to point B, where the electric potential VB = 520 V is greater than the potential at point A. The electric force is the only force acting on the particle. The particle has a speed of 3.90 m/s at point A.
(a) What is its speed at point B?
(b) Is it moving faster or slower at B than at A? Explain why.
Answer:   (a) 4.93 m/s  (b) faster
3.6
Two identical charges with q = +8.00 µC are placed at opposite corners of a square that has sides of length 7.00 cm. Point A is at one of the empty corners, and point B is at the center of the square. A charge q0 = -1.00 µC is placed at point A and moves along the diagonal of the square to point B.
(a) What is the magnitude of the net electric force on q0 when it is at point A?
(b) What is the magnitude of the net electric force on q0 when it is at point B?
(c) How much work does the electric force do on q0 during its motion from A to B? Include a sign to show whether this work is positive or negative.
(d) When it goes from A to B, does q0 move to higher potential or to lower potential? 
Answer:  (a) 20.8 N  (b) 0 N  (c) +0.85 J  (d) higher potential
3.7
(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is 3.00 x 106 V/m, if the plates are separated by 2.00 mm and a potential difference of 5.0 x 103 V is applied?
(b) How close together can the plates be with this applied voltage?
Answer:   (a) No  (b) 1.7 mm
3.8
(a) Find the voltage near a 10.0 cm diameter metal sphere that has 8.00 C of excess positive charge on it.
(b) What is unreasonable about this result?
(c) Which assumptions are responsible?
Answer:  1.4 x 1012 V
3.9
A small spherical pith ball of radius 0.50 cm is painted with a silver paint and then -10 µC of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius 2.0 cm and outer radius 2.2 cm.
(a) Find the electric potential of the gold shell with respect to zero potential at infinity.
(b) How much charge should you put on the gold shell if you want to make its potential 100 V?
Answer:   (a) -4.1 x 106 V   (b) +1.000024 x 10-5 C
3.10
In a particular region, the electric potential is given by V = -xy2z + 4xy. What is the electric field in this region?
Answer: Ex = y2z – 4y, Ey = 2xyz – 4x, Ez = xy2