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A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through each face of the cube?
Concept: Gauss’s Law
Define dipole moment of an electric dipole. Is it a scalar or a vector?
Concept: Electric Dipole
An electric dipole of dipole moment `vecP` is placed in a uniform electric field `vecE` with its axis inclined to the field. Write an expression for the torque `vecT` experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that the torque acting on it is:
- maximum
- Zero
Concept: Dipole in a Uniform External Field
Answer the following question.
Derive an expression for the electric field at any point on the equatorial line of an electric dipole.
Concept: Electric Dipole
The electric flux through a closed Gaussian surface depends upon ______.
Concept: Electric Flux
Derive the expression for the torque acting on an electric dipole, when it is held in a uniform electric field. identify the orientation of the dipole in the electric field, in which it attains a stable equilibrium.
Concept: Dipole in a Uniform External Field
The magnitude of the electric field due to a point charge object at a distance of 4.0 m is 9 N/C. From the same charged object the electric field of magnitude, 16 N/C will be at a distance of ______.
Concept: Electric Field >> Electric Lines of Force
An electric dipole of length 2 cm is placed at an angle of 30° with an electric field 2 × 105 N/C. If the dipole experiences a torque of 8 × 10-3 Nm, the magnitude of either charge of the dipole is ______.
Concept: Dipole in a Uniform External Field
A point charge +Q is placed at point O, as shown in the figure. Is the potential difference VA – VB positive, negative or zero?

Concept: Potential Due to a Point Charge
Two parallel-plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates, while Y contains a dielectric medium of εr = 4.

(i) Calculate capacitance of each capacitor if the equivalent capacitance of the combination is 4 μF.
(ii) Calculate the potential difference between the plates X and Y.
(iii) Estimate the ratio of electrostatic energies stored in X and Y.
Concept: Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates
Three point charges, + Q + 2Q and – 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-point A1, B1 and C1, respectively, find the amount of the work done in shifting the charges to the new locations.

Concept: Electrical Potential Energy of a System of Two Point Charges and of Electric Dipole in an Electrostatic Field
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

Concept: Capacitors and Capacitance
A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if the refractive index of the material of the sphere is \[\sqrt{3}\].

Concept: The Parallel Plate Capacitor
In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10−3m2 and the separation between the plates is 3 mm.
- Calculate the capacitance of the capacitor.
- If this capacitor is connected to 100 V supply, what would be the charge on each plate?
- How would charge on the plates be affected, if a 3 mm thick mica sheet of k = 6 is inserted between the plates while the voltage supply remains connected?
Concept: The Parallel Plate Capacitor
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?
Concept: Capacitors and Capacitance
An electric dipole is held in a uniform electric field.
(i) Show that the net force acting on it is zero.
(ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180°.
Concept: Potential Due to an Electric Dipole
A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.
Concept: Capacitors and Capacitance
Deduce the expression for the electrostatic energy stored in a capacitor of capacitance 'C' and having charge 'Q'.
Concept: Relation Between Electric Field and Electrostatic Potential
How will the (i) energy stored and (ii) the electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant K?
Concept: Relation Between Electric Field and Electrostatic Potential
Draw a plot of potential energy of a pair of nucleons as a function of their separation.
what is the significance of negative potential energy in the graph drawn?
Concept: Conductors and Insulators Related to Electric Field
