PATAUDI’S
VIRAT INSTITUTE
CLASS XII PHYSICS CH – 1 Numericals
1. Two identical point charges of magnitude Q are kept at a distance r from each other. A
third point charge q is placed on the line joining the above two charges, such that all the
three charges are in equilibrium. What is the sign, magnitude and position of the third
charge?
2. Three point electric charges +q each are kept at the vertices of an equilateral triangle of side a.
Determine the magnitude and sign of the charge to be kept at the centroid of the triangle so that
the charges at the vertices remain in equilibrium.
3. Two-point charges 4μC and +1μC are separated by a distance of 2m in air. Find the point on the
line-joining charges at which the net electric field of the system is zero.
4. An electric dipole, when held at 300 with respect to a uniform electric field of
104N/C experiences a torque of 9 x 10-26Nm. Calculate dipole moment of the dipole.
5. Two charges ±10μC are placed 5⋅0 mm apart. Determine the electric field at (a) point P
on the axis of dipole 15cm away from its center on the side of the positive charge. (b) a
point Q. 15cm away from O on a line passing through O and normal to the axis of the
dipole.
6. An electric field is uniform, and in the positive x direction for positive x, and uniform with the
same magnitude but in the negative x direction for negative x. It is given that E=200i^
N/C for x > 0 and E= −200i^ N/C for x < 0. A right circular cylinder of length 20cm and
radius 5cm has its centre at the origin and its axis along the x-axis so that one face is at x= +
10cm and the other is at x= −10cm.
(a) What is the net outward flux through each flat face?
(b) What is the flux through the side of the cylinder?
(c) What is the net outward flux through the side of the cylinder?
7. A particle of mass 9×10-5 g is placed on a uniformly charged long horizontal sheet of
surface charge density of 5×10-5 C/m2. How much should be the charge on the particle so
that it would not fall when left freely?
8. A spherical conductor of radius 12 cm has a charge of 1.6×10-7 C distributed uniformly on its
surface. What is the electric field
(a) inside the sphere
(b) Just outside the sphere
(c) At a point 18 cm from the centre of the sphere?