IIT-JEE 2011 - Career Point

In a conductor, all points have the same potential.
If charge q (coulomb) is placed at a point where the
potential is V (volt), the potential energy of the
system is qV (joule). It follows that if charges q 1 , q 2
are separated by distance r, the mutual potential
q
energy of the system is 1 q 2
4πε r
.
• Relation Between Field (E) And Potential (V)
The negative of the rate of change of potential along
a given direction is equal to the component of the
field that direction.
∂V
E r = – along r
∂ r
∂V and E ⊥ = perpendicular to r
r ∂θ
When two points have different potentials, an electric
field will exist between them, directed from the
higher to the lower potential.
• Lines of Force
A line of force in an electric field is such a curve that
the tangent to it at any point gives the direction of the
field at that point. Lines of force cannot intersect
each other because it is physically impossible for an
electric field to have two directions simultaneously.
• Equipotential Surfaces
The locus of points of equal potential is called an
equipotential surface. Equipotential surfaces lie at
right angles to the electric field. Like lines of force,
they can never intersect.
Note: For solving problems involving electrostatic
units, remember the following conversion factors:
3 × 10 9 esu of charge = 1 C
1 esu of potential = 300 V
• Electric Flux
The electric flux over a surface is the product of its
surface area and the normal component of the electric
field strength on that surface. Thus,
dϕ = (E cos θ) ds = E n ds = → E . → ds
ds
O
The total electric flux over a surface is obtained by
summing :
→ →
→ →
ϕ E = ∑ E . ∆ s or
∫ E .d s
Gauss's Theorem The total electric flux across a
1
closed surface is equal to times the total charge
ε0
inside the surface.
Mathematically ∑ → E . ∆ →
s = q/ε 0
where q is the total charge enclosed by the surface.
E
N
Problems in electrostatics can be greatly simplified
by the use of Gaussian surfaces. These are imaginary
surfaces in which the electric intensity is either
parallel to or perpendicular to the surface everywhere.
There are no restrictions in constructing a
Gaussian surface.
The following results follow from Gauss's law
1. In a charged conductor, the entire charge resides
only on the outer surface. (It must always be
remembered that the electric field is zero inside a
conductor.)
2. Near a large plane conductor with a charge
density σ (i.e., charge per unit area), the electric
intensity is
E = σ/ε 0 along the normal to the plane
3. Near an infinite plane sheet of charge with a
charge density σ, the electric intensity is
E = σ/2ε 0 along the normal to the plane
4. The electric intensity at a distance r from the axis
of a long cylinder with λ charge per unit length
(called the linear density of charge), is
1 λ
→
E = along r
2πε
r
0
Problem solving strategy: Coulomb's Law :
Step 1 : The relevant concepts : Coulomb's law
comes into play whenever you need to know the
electric force acting between charged particles.
Step 2 : The problem using the following steps :
Make a drawing showing the locations of the
charged particles and label each particle with its
charge. This step is particularly important if more
than two charged particles are present.
If three or more charges are present and they do
not all lie on the same line, set up an xycoordinate
system.
Often you will need to find the electric force on
just one particle. If so, identify that particle.
Step 3 : The solution as follows :
For each particle that exerts a force on the particle
of interest, calculate the magnitude of that force
1 | q1q
2 |
using equation F =
2
4πε0 r
Sketch the electric force vectors acting on the
particle(s) of interest due to each of the other
particles (that is, make a free-body diagram).
Remember that the force exerted by particle 1 on
particle 2 points from particle 2 toward particle 1
if the two charges have opposite signs, but points
from particle 2 directly away from particle 1 if the
charges have the same sign.
Calculate the total electric force on the particle(s)
of interest. Remember that the electric force, like
any force, is a vector. When the forces acting on a
charge are caused by two or more other charges,
the total force on the charge is the vector sum of
XtraEdge for IIT-JEE 24 MAY 2010