PHYS 2212 Module 3 Self Assessment Practice Problems
Module 3 Self Assessment Practice Problems
3.1
A nucleus such as lithium contains three protons. We can model this nucleus as an equilateral triangle with a proton at each corner, where each side of the triangle has a length of 2.00 × 10⁻¹⁵ m. If the three protons start out very far apart, how much work is needed to bring them together into this arrangement?
Answer: 3.5 x 10-13 J
3.2
(a) Two protons start at a separation of 2.00 × 10⁻¹⁰ m, a typical distance between atoms. They are pushed together — very slowly, at constant speed — until they reach a separation of 3.00 × 10⁻¹⁵ m, a typical distance within a nucleus. How much work does this take?
(b) Now suppose the two protons are released from rest at the closer separation, 3.00 × 10⁻¹⁵ m. How fast are they moving once they reach their original separation of 2.00 × 10⁻¹⁰ m?
Answer: (a) 7.7 x 10-14 J (b) 6.8 x 106 m/s
3.3
An alpha particle contains two protons and two neutrons. To form a helium atom, this alpha particle is fixed in place, and two electrons are brought in from far away, one at a time. First, one electron is brought in and fixed at a distance of 0.600 × 10⁻¹⁰ m from the alpha particle. Then, a second electron is brought in from far away and fixed at that same distance, 0.600 × 10⁻¹⁰ m from the alpha particle, but on the opposite 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 × 10⁻⁹ C is released from rest at point A, in a region of uniform electric field. The object moves 0.500 m to the right, reaching point B, where it has a kinetic energy of 3.00 × 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 × 10⁻⁴ kg. It moves from point A, where the electric potential is VA = 270 V, to point B, where the electric potential is VB = 520 V. The electric force is the only force acting on the particle, and its speed at point A is 3.90 m/s.
(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 of q = +8.00 µC are placed at opposite corners of a square with sides of length 7.00 cm. Point A is at one of the two empty corners, and point B is at the center of the square. A third charge, q₀ = −1.00 µC, is placed at point A and moves along the diagonal 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 lower potential?
Answer: (a) 20.8 N (b) 0 N (c) +0.85 J (d) higher potential
3.7
(a) Two parallel conducting plates are separated by 2.00 mm, with a potential difference of 5.0 × 10³ V applied between them. Dry air breaks down — meaning it stops acting as an insulator — once the electric field strength reaches 3.00 × 10⁶ V/m. Will the electric field between the plates exceed this breakdown strength?
(b) With this same 5.0 × 10³ V applied, how close together could the plates be without the field exceeding the breakdown strength?
Answer: (a) No (b) 1.7 mm
3.8
A metal sphere with a diameter of 10.0 cm carries 8.00 C of excess positive charge.
(a) Find the voltage at the surface of the sphere.
(b) What is unreasonable about this result?
(c) Which assumptions are responsible for this unreasonable result?
Answer: 1.4 x 1012 V
3.9
A small spherical pith ball with a radius of 0.50 cm is coated with silver paint and then given a charge of −10 µC. This charged ball is placed at the center of a gold spherical shell with an inner radius of 2.0 cm and an outer radius of 2.2 cm.
(a) Find the electric potential of the gold shell, taking the potential to be zero at infinity.
(b) How much charge should you put on the gold shell if you want its potential to be 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?
Physics Education Research at UNG 