Electric Charges and Fields 4

Question 1

what is
i) linear charge density
ii) surface charge density
iii) volume charge density or charge density

Answer 1

λ=Q/l
charge per unit length

σ = S/ A
charge per unit area

ρ= Q/V
charge per unit volume

At the microscopic level, charge distribution is discontinuous, because they are
discrete charges separated by intervening space where there is no charge.
at macroscopic level charges can be taken to be continuous

Question 2

define electric flux

Answer 2

electric flux is the number of electric field lines passing normally through a given surface area and it is measured as the product of electric field and area vector ds

phi= E. ds
Eds cos theta

Question 3

what is area vector

Answer 3

area is not a scalar quantity, it also has a direction

the direction of a planar area vector is along its normal.

vector associated with every area element of a closed surface is taken
to be in the direction of the outward normal.

How to associate a vector to the area of a curved surface? We imagine
dividing the surface into a large number of very small area elements.
Each small area element may be treated as planar and a vector associated
with it

Question 4

state gauss law

Answer 4

The flux through a closed surface is equal to 1/ epsilon not times the total charge enclosed by the surface
ɸ= q/ε0

Answer 5

(i) Gauss’s law is true for any closed surface, no matter what its shape
or size.
(ii) The term q on the right side of Gauss’s law, Eq. (1.31), includes the
sum of all charges enclosed by the surface. The charges may be located
anywhere inside the surface.
(iii) In the situation when the surface is so chosen that there are some
charges inside and some outside, the electric field [whose flux appears
on the left side of Eq. (1.31)] is due to all the charges, both inside and
outside S. The term q on the right side of Gauss’s law, however,
represents only the total charge inside S.

The surface that we choose for the application of Gauss’s law is called
the Gaussian surface. You may choose any Gaussian surface and
apply Gauss’s law. However, take care not to let the Gaussian surface
pass through any discrete charge. This is because electric field due
to a system of discrete charges is not well defined at the location of
any charge. (As you go close to the charge, the field grows without
any bound.) However, the Gaussian surface can pass through a
continuous charge distribution.