IIT-JEE 2011 - Career Point

the indivual forces. It's often helpful to use
components in an xy-coordinate system. Be sure
to use correct vector notation; if a symbol
represents a vector quantity, put an arrow over it.
If you get sloppy with your notation, you will also
get sloppy with your thinking.
As always, using consistent units is essential.
With the value of k = 1/4πε 0 given above,
distances must be in meters, charge in coulombs,
and force in newtons. If you are given distance in
centimeters, inches, or furlongs, donot forget to
convert ! When a charge is given in
microcoulombs (µC) or nanocoulombs (nC),
remember that 1µC = 10 –6 C and 1nC = 10 –9 C.
Some example and problems in this and later
chapters involve a continuous distribution of
charge along a line or over a surface. In these
cases the vector sum described in Step 3 becomes
a vector integral, usually carried out by use of
components. We divide the total charge
distribution into infinitesimal pieces, use
Coulomb's law for each piece, and then integrate
to find the vector sum. Sometimes this process
can be done without explicit use of integration.
In many situations the charge distribution will be
symmetrical. For example, you might be asked to
find the force on a charge Q in the presence of
two other identical charges q, one above and to
the left of Q and the other below and to the left of
Q. If the distance from Q to each of the other
charges are the same, the force on Q from each
charge has the same magnitude; if each force
vector makes the same angle with the horizontal
axis, adding these vectors to find the net force is
particularly easy. Whenever possible, exploit any
symmetries to simplify the problem-solving
process.
Step 4 : your answer : Check whether your numerical
results are reasonable, and confirm that the like
charges repel opposite charges attract.
Problem solving strategy : Electric-field calculations
Step 1: the relevant concepts : Use the principle of
superposition whenever you need to calculate the
electric field due to a charge distribution (two or
more point charges, a distribution over a line, surface,
or volume or a combination of these).
Step 2: The problem using the following steps :
Make a drawing that clearly shows the locations
of the charges and your choice of coordinate axes.
On your drawing, indicate the position of the field
point (the point at which you want to calculate the
electric field E r ). Sometimes the field point will
be at some arbitrary position along a line. For
example, you may be asked to find E r at point on
the x-axis.
Step 3 : The solution as follows :
Be sure to use a consistent set of units. Distances
must be in meters and charge must be in
coulombs. If you are given centimeters or
nanocoulombs, do not forget to convert.
When adding up the electric fields caused by
different parts of the charge distribution,
remember that electric field is a vector, so you
must use vector addition. Don't simply add
together the magnitude of the individual fields:
the directions are important, too.
Take advantage of any symmetries in the charge
distribution. For example, if a positive charge and
a negative charge of equal magnitude are placed
symmetrically with respect to the field point, they
produce electric fields of the same magnitude but
with mirror-image directions. Exploiting these
symmetries will simplify your calculations.
Must often you will use components to compute
vector sums. Use proper vector notation;
distinguish carefully between scalars, vectors, and
components of vectors. Be certain the
components are consistent with your choice of
coordinate axes.
In working out the directions of E r
vectors, be
careful to distinguish between the source point
and the field point. The field produced by a point
charge always points from source point to field
point if the charge is positive; it points in the
opposite direction if the charge is negative.
In some situations you will have a continuous
distribution of charge along a line, over a surface,
or through a volume. Then you must define a
small element of charge that can be considered as
a point, finds of all charge elements. Usually it is
easiest to do this for each component of E r
separately, and often you will need to evaluate
one or more integrals. Make certain the limits on
your integrals are correct; especially when the
situation has symmetry, make sure you don't
count the charge twice.
Step 4 : your answer : Check that the direction of E r
is reason able. If your result for the electric-field
magnitude E is a function of position (say, the
coordinate x), check your result in any limits for
which you know what the magnitude should be.
When possible, check your answer by calculating it
in a different way.
Problem solving strategy : Gauss's Law
Step 1 : Identify the relevant concepts : Gauss's law
is most useful in situations where the charge
distribution has spherical or cylindrical symmetry or
is distributed uniform over a plane. In these situations
we determine the direction of E r from the symmetry
of the charge distribution. If we are given the charge
distribution. we can use Gauss's law to find the the
magnitude of E r . Alternatively, if we are given the
field, we can use Gauss's law to determine the details
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