ththPC1143 Tutorial 1 (16 Jan – 20 Jan 12)
Question 1: Electric charge and electric field Two charges are placed as shown in Figure 1.
3.00，CThe magnitude of is , but its sign and the value of the charge are not known. qq12
EThe direction of the net electric field at point P is entirely in the negative y-direction. (a) Considering the different possible signs of and , there are four possible diagrams qq12
that could represent the electric fields and produced by and . Sketch the four EEqq1212
possible electric field configurations.
E(b) Using the sketches from part (a) and the direction of , deduce the signs of and . qq12
E(c) Determine the magnitude of .
Question 2: Electric charge and electric field Two thin rods of length L lie along the x-axis, one between and and the x！a2x！a2？L
other between and . Each rod has positive charge Q distributed x！？a2x！？a2？L
uniformly along its length.
(a) Calculate the electric field produced by the second rod at points along the positive x-axis. (b) Show that the magnitude of the force that one rod exerts on the other is
a，，L(c) Show that if , the magnitude of this force reduces to
Interpret this result.
1 Physics Department, National University of Singapore (2012)
Question 3: Electric charge and electric field
Positive charge Q is uniformly distributed around a semicircle of radius a.
Find the electric field (magnitude and direction) at the centre of curvature P.
Question 4: Electric potential
A solid sphere of radius R contains a total charge Q distributed uniformly throughout its
volume. Find the energy needed to assemble this charge by bringing infinitesimal charges from far away. This energy is called the “self-energy” of the charge distribution.
Question 5: Electric potential
A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in
a roll of toilet paper) has charge Q uniformly distributed over its surface.
(a) Calculate the electric potential at all points along the axis of the tube. Take the origin to
be at the centre of the tube, and take the potential to be zero at infinity.
L，，R(b) Show that if , the result of part (a) reduces to the potential on the axis of a ring of
charge of radius R.
(c) Use the result of part (a) to find the electric field at all points along the axis of the tube.
AY 2002 – 03, Question 1
(a) Determine the magnitude and direction of the electric field for points on the axis of a
uniform ring of positive charge Q and radius a.
(b) Show that the maximum values of the electric field occur at a distance x！?a2. Here,
x denotes the distance between a point on the axis and the centre of the ring. (c) If an electron of mass m is placed at the centre of the ring and is then displaced a small
distance x along the axis , determine its oscillating frequency. ;；x，，a
2 Physics Department, National University of Singapore (2012)
AY 2002 – 03 Question 2
(a) Derive an expression for the amount of work required to assemble five identical point
charges of magnitude Q at the corners of a regular pentagon of side a.
(b) A solid sphere of radius R has a uniform charge density and total charge Q. Derive an ~
expression for its total electric potential energy.
AY 2003 – 04, Short Question 1
One particle with a charge of is fixed in place at the origin, and another particle q！？8q1
with charge is fixed in place along the horizontal axis at . At what position x！Lq！？2q2
(other than infinity) can a single positive charge be placed so that it is in equilibrium? Is this
a position of stable or unstable equilibrium along the x axis?
AY 2003 – 04, Long Question 6
？QA uniformly charged ring of radius a has a total charge of , as shown below.
Point P is located on the perpendicular central axis of the ring, labelled the x axis.
(a) By summing the contribution to the total electric field by each charge element dq, find an
expression for the magnitude of the electric field at point P and state its direction. Derive
from this an expression for the electric potential at point P.
(b) By summing the contribution to the total electric potential by each charge element dq,
find an expression for the electric potential at point P. Derive from this an expression for
the electric field at point P.
(c) Plot the magnitude of the electric field and the electric potential for positive values of x.
Identify where each is equal to zero and where each has a maximum or minimum value.
3 Physics Department, National University of Singapore (2012)
AY 2004 – 05, Short Question 2
An electron starts from rest 3.00 cm from the centre of a uniformly charged insulating sphere
of radius 2.00 cm and total charge of 1.0 nC. What is the speed of the electron when it
reaches the surface of the sphere?
AY 2005 – 06, Long Question 6
(a) Two identical beads each have a mass m and charge q. When placed in a hemispherical
bowl of radius R with frictionless, non-conducting walls, the beads move and at
equilibrium they are a distance R apart. Find an expression for the charge on each bead.
R！60.0cm(b) A line of positive charge is formed into a semicircle of radius , as shown
The charge per unit length along the semicircle is given by . The total charge ；！；cos；0
12.0，C3.0，Con the semicircle is . Calculate the total force acting on a charge of
y！0placed at the centre of curvature (i.e. the coordinate x！0, in the above figure).
4 Physics Department, National University of Singapore (2012)