Question 1 1 / -0
The displacement of a charge Q in the electric field
= e
1 + e
2 + e
3 is
= a
+ b
. The work done is
Question 2 1 / -0
A parallel plate condenser with a dielectric of dielectric constant, K between the plates has a capacity, C and is charged to a potential, V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is:
Question 3 1 / -0
Two equally charged identical metal spheres A and B repel each other with a force F. The spheres are kept fixed with a distance r between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is :
Question 4 1 / -0
A spherical capacitor consists of an inner sphere of diameter 6 cm and an outer sphere of diameter 10 cm. The space between the two concentric spheres is filled with a medium of dielectric constant 80. What is the capacitance of the capacitor?
Question 5 1 / -0
A pendulum bob of mass 80 milligrams, which is carrying a charge of 2 x 10
-8 C, is at rest in a uniform horizontal electric field of 20,000 V/m. What angle (
) will it make with the vertical?
Solution
At equilibrium,
T cos
θ = mg --- (1)
T sinθ = qE --- ( 2)
Dividing (2) by (1), we get:
Question 6 1 / -0
Three point charges of 1 C, 2 C and 3 C are placed at the corners of an equilateral triangle of side 1 m. The work done (in joules) in bringing these charges to the vertices of a smaller similar triangle of side 0.5 m is
Question 7 1 / -0
A charged particle is suspended in equilibrium in a uniform vertical electric field of intensity 20000 V/m. If the mass of the particle is 9.610 x 10-16 kg, the charge on it and excess number of electrons on the particle respectively are (g = 10 m/s2 )
Question 8 1 / -0
Three charges 1
C, 1
C and 2
C are respectively kept at the vertices A, B and C of an equilateral triangle ABC of side 10 cm. The resultant force on the charge at C is
Solution
Here, F
CA = F
CB = F
C Hence, the resultant force on the charge at C is
Question 9 1 / -0
An insulator plate is passed through the plates of a capacitor as shown. The current
Solution
As insulator plate is passed between the plates of the capacitor, its capacity increases first and then decreases as the plate slips out. As a result, positive charge on plate A increase first and then decreases, hence, current in outer circuit flows from B to A and then from A to B.
Question 10 1 / -0
Eight drops of mercury of equal radii, each having the same charge, combine to form a big drop. The capacitance of this big drop as compared to that of each smaller drop is
Solution
2 times
Volume of big drop = 4/3
R
3 = 8 x 4/3
r
3 R = 2r
Capacitance of big drop = 2 x capacitance of small drop
Question 11 1 / -0
If 1000 drops of water of same radius r and same charge q combine to form a big drop, then how many times is the potential of the big drop relative to the potential of a small drop?
Question 12 1 / -0
The top of the atmosphere is about 400 kV with respect to the surface of Earth corresponding to an electric field that decreases with altitude. Near the surface of Earth, the field is about 100 Vm-1 . Still, we do not get an electric shock as we step out of house into an open space because (assume the house to be a steel cage so that there is no field inside)
Solution
Since our body and the surface of earth both are conducting therefore our body and the ground form an equipotential surface. As we step out into the open from our house the original equipotential surfaces of open air change, keeping out body and the ground at the same potential that is why we donot get an electric shock.
Question 13 1 / -0
A spherical capacitor has an inner sphere of radius 9 cm and an outer sphere of radius 10 cm. The outer sphere is earthed. Assuming that there is air in the space between the spheres, what is the capacitance of the capacitor?
Solution
Capacity of the spherical capacitor,
where a = 0.09 m (inner radius) and b = 0.1 m (outer radius)
Question 14 1 / -0
The potential at a point x (measured in
m) due to some charges situated on the x-axis is given by V(x) = 20/(x
2 - 4) volts. The electric field E at x = 4
m is given by
Solution
E = -
=
2x
=
× (2
×
4)
=
volts/
m along the positive x-direction
Question 15 1 / -0
A capacitor having capacitance of 1 µF in air is filled with two dielectrics as shown. How many times will the capacitance increase?
Question 16 1 / -0
Two point charges 3 × 10-6 C and 8 × 10-6 C repel each other by a force of 6 × 10-3 N. If each of them is given an additional charge of -6 × 10-6 C, then the force between them will be
Question 17 1 / -0
A charged particle q moving with speed v is shot towards another charged particle Q, which is held stationary. It approaches Q up to a closest distance r and then returns. If q was given a speed of 2v, what will be the closest distance approached by this charge?
Solution
Let a particle of charge q having velocity v approach Q upto a closest distance r and if the velocity becomes 2v, the closest distance will be r.
The law of conservation of energy yields, kinetic energy of particle = electric potential energy between them at closest distance of approach.
or
and
Dividing equation (i) by equation (ii),
⇒
⇒
Question 18 1 / -0
If the inward flux and outward electric flux from a closed surface respectively are 8 × 103 units and 4 × 103 units, then what is the net charge inside the closed surface?
Question 19 1 / -0
An electric charge of 10
-3 μC is placed at the origin (0, 0) of an X-Y coordinate system. Two points A and B are at (
,
) and (2, 0), respectively. The potential difference between the points A and B will be
Solution
Distance of the point A from origin is,
Distance of the point B from origin is 2 m.
Since both points A and B are at the same distance from the charge placed at the origin, they will have same potential and potential difference between A and B will be zero.
Question 20 1 / -0
The electric flux for Gaussian surface A that encloses the charged particles in free space is (given q
1 = - 14 nC, q
2 = 78.85 nC,q
3 = - 56 nC)
Question 21 1 / -0
A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at point P, at a distance R/2 from the centre of the shell, is
Question 22 1 / -0
A hollow metal sphere has an inner radius of 10 cm and an outer radius of 20 cm. This hollow metal sphere carries no net electric charge. A small solid metal bell of radius 1.0 cm is located at the centre of the hollow sphere. The metal ball carries a positive charge of 200 nC. What is the electric charge (nC) on the outer surface of the hollow metal sphere?
Solution
For a conducting shell if we place a charge inside the shell it will be reflected at the outer surface of the shell. Hence charge on the outer surface is 200nC
Question 23 1 / -0
A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result, the potential difference between the plates
Solution
For the parallel plate capacitor, the capacitance is given by:
When the battery is disconnected, the charge remains constant. As the separation between the plates is increased, the capacitance decreases, and voltage across the capacitor will increase as we have:
Question 24 1 / -0
Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them, so that the electric potential energy of the system is minimum?
Question 25 1 / -0
Two identical capacitors, each of capacitance 5 µF, are charged to potentials 2 kV and 1 kV. Their negative ends are connected together. When the positive ends are also connected together, what is the loss of energy of the system?
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