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Tutorial 1 (28th Jan.. - National University of Singapore

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Tutorial 1 (28th Jan.. - National University of Singapore

    PHYSICS III

    ththPC1143 Tutorial 1 (16 Jan 20 Jan 12)

    Question 1: Electric charge and electric field Two charges are placed as shown in Figure 1.

    Figure 1

    3.00CThe 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 xa2xa2L

    other between and . Each rod has positive charge Q distributed xa2xa2L

    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

    22?(Q;;aLFln ?)2;;4:(Laa2L0??

    a,,L(c) Show that if , the magnitude of this force reduces to

    2Q F24:(a0

    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.

    Figure 2

    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 q8q1

    with charge is fixed in place along the horizontal axis at . At what position xLq2q2

    (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.

    R60.0cm(b) A line of positive charge is formed into a semicircle of radius , as shown

    below.

    The charge per unit length along the semicircle is given by . The total charge cos0

    12.0C3.0Con the semicircle is . Calculate the total force acting on a charge of

    y0placed at the centre of curvature (i.e. the coordinate x0, in the above figure).

    4 Physics Department, National University of Singapore (2012)

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