Raj is visiting the United States and needs to convert 2,000 rupees to US dollars.
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By Stokes' theorem, the line integral of over
is given by the surface integral of the curl of
over
, where
is the region of intersection of the plane
and the cylinder
with
having positive/upward orientation.
Parameterize by
with and
.
Take the normal vector to to be
The curl of is
Then the line integral is equivalent to
Answer:
See below
Step-by-step explanation:
(a) Field lines
A negatively charged particle has an electric field associated with it.
The field lines spread out radially from the centre of the point. They are represented by arrows pointing in the direction that a positive charge would move if it were in the field.
Opposite charges attract, so the field lines point toward the centre of the particle.
For an isolated negative particle, the field lines would look like those in Figure 1 below.
If two negative charges are near each other, as in Figure 2, the field lines still point to the centre of charge.
A positive charge approaching from the left is attracted to both charges, but it moves to the closer particle on the left.
We can make a similar statement about appositive charge approaching from the left.
Thus, there are few field lines in the region between the two particles.
(b) Coulomb's Law
The formula for Coulomb's law is
F = (kq₁q₂)/r²
It shows that the force varies inversely as the square of the distance between the charges.
Thus, the force between the charges decreases rapidly as they move further apart.
