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PHYS1022 Synoptic examples
1. A charge q is at the point x = 1 m, y = 0. Write expressions for the unit vectors you
would use in Coulomb’s law if you were finding the force that q exerts on other charges
located at
a) x = 1 m, y = 1 m,
b) the origin,
c) x = 2 m, y = 3 m.
Note that you don’t know the sign of q. Why doesn’t this matter?
2. A proton is at the origin and an electron is at the point x = 0.41 nm, y = 0.36 nm. Find
the electric force on the proton.
3. Three identical charges +q and a fourth charge –q form a square of side a.
(a) Find the magnitude of the electric force on a charge Q placed at the centre of
the square.
(b) Describe the direction of this force.
4. (B question)The figure shows a thin, uniformly charged disk of
radius R. Imagine the disk divided into rings of varying radii r, as
shown.
Show that the net electric field on the disk axis has magnitude


x
E  2 k 1 

x2  R2 

5. An electron close to a large, flat sheet of charge is repelled from the sheet with a force
of 1.8 × 10−12 N. Find the surface charge density of the sheet using Gauss’s law.
6. A coaxial cable consists of a 2.0 mm diameter inner conductor and an outer conductor
of diameter 1.6 cm and negligible thickness. If the conductors carry line charge densities
of ±0.56 nC/m, what is the magnitude of the potential difference between them?
7. Two conducting spheres are each 5.0 cm in diameter and each carries 0.12 μC. They
are 8.0 m apart. Determine
(a) the potential at the surface of each sphere
(b) the field strength at the surface of each sphere
(c) the potential midway between the spheres
(d) the potential difference between the spheres.
8. Find the capacitance of a long cylindrical conductor with radius a, and linear charge
density λ, surrounded by a coaxial cylindrical conducting shell with inner radius b, and
linear charge density –λ.
9. A capacitor consists of a conducting sphere of radius a, surrounded by a concentric
conducting shell of radius b. Show that its capacitance is:
ab
C  4 0
ba
10. An electron moving at velocity v in the x direction through a magnetic field which is
uniform and in the –z direction with magnitude B = 0.10 T experiences an acceleration of
6.0 × 1015 m/s2.
(a) Find the force on the electron
(b) What is the electron’s speed?
(c) By how much does its speed change in 1 ns?
11. The magnitude of the Earth’s magnetic field is a little less than 1 G (or 10-4 T) near
the Earth’s surface. What is the maximum possible magnetic force on an electron with
kinetic energy of 1 keV?
Compare with the gravitational force on the same electron.
12. A particle carrying a 50 μC charge moves with velocity v = 5.0i + 3.2k m/s through a
uniform magnetic field B = 9.4k + 6.7j T.
(a) Find the magnetic force on the particle.
(b) Form the dot products F.v and F.B to show explicitly that the force is perpendicular to
both v and B.
13. A current carrying wire is bent into a semicircular loop of radius R that lies in the xy
plane. There is a uniform magnetic field B perpendicular to the plane of the loop in the zdirection. Verify that the force acting on the loop is zero.
14. The wire segment shown in the figure carries a current of 1.8 A
from a to b. There is a magnetic field B = 1.2 T in the z-direction.
Find the total force on the wire and show that the total force is the
same as if the wire were a straight segment from a to b.
15. A wire of negligible resistance is bent into the rectangle
in the circuit shown. The right hand side extends into a
region of uniform magnetic field of 38 mT pointing into the
page. Find the magnitude and direction of the net force on
the circuit.
16. A conducting rod of length 20 cm and mass 18 g is suspended by wires of negligible
mass. The rod is in a region of a uniform magnetic field of 0.15 T pointing into the page.
An external circuit supplies current between the supports A and B.
(a) What is the minimum current needed to move the bar to the
upper position, so that it is supported by gravity?
(b) In which direction should the current flow?
17. A single piece of wire is bent so that it includes a
circular loop of radius a. A current I flows in the
direction shown. Find an expression for the magnetic
field at the centre of the loop.
18. (B question) A long straight wire carries 20 A. A
rectangular wire loop 5.0 × 10 cm carries current of 500 mA
and is located 2.0 cm from the wire as shown. Find the net
magnetic force on the loop.
Note: name each dimension in the figure before starting and
use algebra throughout your answer.
Now find an expression for the magnetic flux through the rectangular loop due to current
I1 in the long wire.
19. A conducting loop of area 240 cm2 and resistance 12 Ω lies at right angles to a
spatially uniform magnetic field. The loop carries an induced current of 320 mA. At what
rate is the magnetic field changing?
20. The magnetic field inside a 20 cm diameter solenoid is increasing at a rate of 2.4 T/s.
How many turns should a coil wrapped around the outside of the solenoid have so that
the emf induced in the coil is 15 V?
21. A square wire loop with sides of 3.0 m is perpendicular to a uniform magnetic field of
2.0 T. A 6.0 V light bulb is in series with the loop. The magnetic field is reduced steadily
to zero over time ∆t.
(a) Find ∆t such that the light will shine at full brightness during this time.
(b) Which way will the loop current flow?
22. Three resistors are in series surrounding an infinitely long solenoid with a changing
magnetic field; the resulting induced electric field drives a
current counter-clockwise, as shown. Two identical voltmeters
are connected to the same points A and B. What does each read?
Explain any apparent contradiction.