Physics 2: Physical Science & Technology (PHYC10004)
Week 4
Discussion Questions
1
The diagram shows eight particles that form a square, with distance d between adjacent particles. What is the net electric potential at point P at the centre of the square (take the electric potential to be zero at infinity)?
Halliday, David. Fundamentals of Physics Extended, 10th Edition. John Wiley & Sons
2
A positive point charge of magnitude q0 is shown in the figure.
(a) Points B and C are located at a distance r from the charge. Point A is at a distance 2r.
(i) Indicate the direction of the electric field at points A, B and C in the figure.
(ii) Compared to the absolute value of the work done in moving a small test charge from A to B: would the absolute value of this work done in moving the same test charge from B to C be larger, smaller, or the same?
(iii) Would the absolute value of the work done in moving the same test charge from A to C be larger, smaller, or the same?
(b) A large metal sphere with zero net charge is now placed to the left of point A, as shown.
(i) Sketch the charge distribution on the metal sphere in the figure.
(ii) Has the magnitude of the electric field at points B and C increased, decreased, or remained the same? Explain.
(iii) Has the direction of the electric field at the points B and C changed? Explain.
(iv) Has the value of the electric potential VA and at VB increased, decreased, or remained the same?
Reproduced from Tutorials in Introductory Physics, LC McDermott et al. © Prentice-Hall 2002
3
A solid conducting sphere of radius 1.0 m is given a charge of +(4/9)π coulombs throughout its volume and allowed to reach equilibrium.
(a) What is the field and potential at its centre?
(b) Would your answer change if the sphere was an insulator? In what way(s)?
4
A parallel-plate capacitor is connected to a battery of electric potential difference V. If the plate separation is decreased, do the following quantities increase, decrease, or remain the same?
(a) the capacitor’s capacitance,
(b) the voltage across the capacitor,
(c) the charge on the capacitor,
(d) the magnitude of the electric field between the plates.
5
Repeat the previous question for the case when the capacitor is first charged, and then disconnected from the battery. Do your answers change?
From Fundamentals of Physics Extended, 10th Edition. John Wiley & Sons
Problem-solving Questions
6
An electron in a TV picture tube is accelerated along the electric field (assumed uniform) between the filament and the screen, a distance of 50 cm. The field does 4.8 × 10-15 J of work on the electron. Assume the field is uniform.
a) Calculate the potential difference between filament and screen.
b) Calculate the electric field strength.
c) Calculate the force on the electron just after the filament? Just before the screen?
Halliday, David. Fundamentals of Physics Extended, 10th Edition. John Wiley & Sons
7
Water molecules have a permanent dipole moment of 6.2 × 10–30 C m. In a uniform electric field of 5 × 106 V m–1, calculate the:
• maximum torque that this field could cause, and
• the greatest change of electrical potential energy that could occur.
8
Find the potential at the centre of a copper ring with a charge density of 25 pC/m.
9 (mini-challenge question 1)
Two very large plates with area A1 are held a distance d apart and have net charges -Q and +Q. Assume that all the charge is uniformly distributed on the inner surfaces ofthe plates.
a) Write an expression for the capacitance C in terms ofA1, d and ε0.
Two initially uncharged plates of surface area A2 are then attached to the original plates as shown to the right. Assuming d is very small.
b) Find the charge density on the plates and the voltage between them.
c) The right plate is now moved to the right, increasing the separation to D (still relatively small). Describe how each of the following quantities will change (if at all):
• the charge density on each plate
• the electric field both outside and between the plates
• the potential difference between the plates.
Reproduced from Tutorials in Introductory Physics, LC McDermott et al. © Prentice-Hall 2002
10 (mini-challenge question 2)
The diagram shows a non-conducting rod of length L with charge -q uniformly distributed along its length. The linear charge density on the rod is given by λ and is equal to –q/L.
Calculate the electric potential at point P, a distance a from the end ofthe rod.
(NOTE an integration is required.)
Past examination questions
11
(a) A metal sphere of radius 20 cm has a net charge of -20 nC. There are no other charges present.
(i) What are the magnitude and direction of the electric field at the surface of the sphere?
(ii) Assuming that the electric potential is zero at infinity, what is the electric potential at the sphere’s surface?
(iii) If an electron is released from a point at the surface of the sphere, and the force due to the sphere is the only force acting on it, how much kinetic energy does the electron gain as it is repelled from the surface?
(b) Determine the magnitude of the potential difference across each capacitor in the figure.
12
(a) Two identical capacitors with capacitance C, each carrying a charge Q, are connected as shown in the figure. A piece of dielectric material with a dielectric constant of K is inserted and completely fills the gap between the plates of one of the capacitors.
Write down an expression for the new charge Q’ on that capacitor.