Electric charges and fields
Electric
Charges And Fields
Problems
Question
1. Draw a diagram to show lines of force in a plane containing two equal point
charges of opposite sign separated by a small distance. Giving reason, indicate
on the diagram a point where a small positive charge experiences a force
parallel to the line joining the two charges.
Solution. As
shown in the above figure, electric field at any point P on the equatorial line
is parallel to the line joining the two charges. So if a small positive charge
is placed at such a point, it will experience a force parallel to the line join
in the two charges.
Question
2. What is meant by the statement that the electric field of a point charge has
spherical symmetry whereas that of an electric dipole is cylindrical symmetric?
Solution. The electric field due to a point charge q at distance r from it is given by
Question 3.
An electric dipole free to move is placed in a uniform electric field. Explain
along with diagram its motion when it is placed,
(a) Parallel
to the field.
(b) Perpendicular
to the field.
Solution. (a) Since the
line of action of the two forces passes through the same point, the net force
and the net torque acting on the dipole is zero. So no motion is produced when
a dipole is placed to the electric field.
Solution:
The directions of the two dipole moments and their resultant are shown in the
above figure.
Question 7. (a) Define electric
flux. Write its SI Units. A spherical balloon carries a charge that is uniformly
distributed over its surface. As the balloon us blown up and increases in size,
how does the total electric flux coming out of the surface change? Give reason.
Solution: (a) The electric flux
through a given surface area is the total number of electric lines of force
passing normally through that area.
As the balloon is blown up and increases in
size, the total charge on its surface remains constant. Hence, by Gauss’s
theorem, the electric flux coming out of its surface remains unchanged.
Find
(i)The force on the charge at
the centre of shell and at the point A,
(ii)The electric flux through
the shell.
Solution. Net force on the charge Q/2
placed at the centre of the shell is zero.
Force in the charge 2Q kept at point A
at distance r from the centre is
Question 9. Two thin concentric
and co-planar spherical shells, of radii a and b (b ˃ a) carry charges q and Q,
respectively. Find the magnitude of the electric field, at a point distant
(i) 0 <
(i) For a <
(ii)For b <
Question 10. A spherical rubber
balloon carries a charge that is uniformly distributed over its surface. As the
balloon is blown up ; how does E vary for points (i) inside the balloon, (ii)
on the surface of the balloon and (iii) outside the balloon ?
Solution. (i) For points inside the balloon, E=0.
(iii) For points outside the balloon,
As the balloon is blown up, the charge
enclosed by the Gaussian surface remains same, so E does not change.
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