Video Lecture
Theory For Notes Making
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Objective Assignment
Q. 1
An electric dipole placed in a uniform electric field experiences, in general
(a) a force and a torque
(b) a force only
(c) a torque only
(d) neither a force nor a torque
Ans. (c)
Q.2
A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. And B are far away from the dipole and at equal distances from it. The fields at A and B are A and B.
(a) A = B
(b) A=2B
(c) A=-2B
(d) |EB|=1/2|EA|, and B perpendicular to A
Ans. (c)
Q.3
an electric dipole of moment is placed in a uniform electric field , with parallel to . It is then rotted by an angle q. The work done is
(a) pE sin q
(b) pE cosq
(c) pE(1-cosq)
(d) pE(1-sin T)
Ans. (c)
Q. 4
In which of the following states is the potential energy of an electric dipole maximum ?
Ans (a)
Q.5
An electric dipole of moment p is placed normal to the lines of force of electric field E, then the work done in deflecting it through an angle of 180 degrees is
(1) pE
(2) + 2pE
(3) –
(4) Zero
Ans. (4)
Q.6
An electric dipole is placed in an uniform electric field such that the dipole moment makes an angle b ( ¹ 0) with The force and torque acting on the dipole are respectively given by
(1) \displaystyle 0,\,\,\overrightarrow{{p\,}}\times \overrightarrow{{E\,}}
(2) \displaystyle \overrightarrow{{p\,}}\cdot \overrightarrow{{E\,}},\,\,\,\overrightarrow{{p\,}}\times \overrightarrow{{E\,}}
(3) \displaystyle \overrightarrow{{p\,}}\times \overrightarrow{{E\,}},\,\,0
(4) \displaystyle \overrightarrow{{p\,}}\times \overrightarrow{{E\,}},\,\,\overrightarrow{{E\,}}\times \overrightarrow{{p\,}}
Ans. (1)
Q.7
An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct?
(1) Electric flux is coming towards sphere
(2) Electric flux is coming out of sphere
(3) Electric flux entering into sphere and leaving the sphere are same
(4) Water does not permit electric flux to enter into sphere.
Ans. (3)
Subjective Assignment
Q.1
Find the force acting on a proton, which is placed 10cm from a short dipole of dipole moment 10 Cm along the axis.
Q.2
Two short dipoles of moment P1= 10Cm and P2 = 20 Cm are kept perpendicular to each other. Find the electric field at a point O midway between them.
Q.3
A dipole of moment 10 Cm is placed in a uniform electric field of 2000N/C at an angle of 30.Find the force and torque acting on the dipole.
Q.4
A dipole is kept in the position of least energy in a uniform electric field E. When the dipole is slightly displaced from its position and released it is found to oscillate about the initial position. If I is the moment of inertia of the dipole find the time period of oscillations.
Q.5
Two short dipoles are placed parallel to each other at a distance of 2 cm. If each of them have a dipole moment of 10Cm find the torque acting on one due to other.
Q.6
An electric dipole consists of charges of 1.5nC separated by 6.2mm is in an electric field of 1100 N/C. What is the difference of the potential energy of this dipole in stable and unstable equilibrium?
Q.7
A molecule of a substance has permanent electric dipole moment equal to 10-29 C-m. A mole of this substance is polarised (at low temp.) by applying a strong electrostatic field of magnitude 106 V m-1. The direction of the field is suddenly changed by an angle of 60°. Estimate the heat released by the substance in aligning its dipoles along the new direction f the field, assume 100% polarization of the substance.
Q.8
Two charges of ±0.2 mmC and -0.2mmC are placed 10-6 cm apart. Calculate the electric field at an axial point at a distance of 10 cm from their middle point. Use the standard value of Î0.
Q.9
Calculate the magnitude of the force, due to an electric dipole of dipole moment 3.6×10-29 C-m, on an electron 25 nm from the centre of the dipole, along the dipole axis. Assume that this distance is large relative to the dipole’s charge separation.
Q.10
Two charges ±10 mC are held 5 mm apart. Calculate the dipole moment. What is electric field intensity due to this dipole at a distance of 15 cm from the centre of the dipole on the axial line of the dipole?
Q.11
An electric dipole consists of two charges of 0.1 mC separated by a distance of 2.0 cm. The dipole is placed in an external field of 105 N/C. What maximum torque does the field exert on the dipole?
Q.12
Two charges each of 1 m C but opposite in sign are 1 cm apart. Calculate electric field at a point distant 10 cm from the mid point on axial line of the dipole.
Q.13
In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium ?
Q.14
Write the expression for the work done on an electric dipole of dipole moment \displaystyle \vec{p} in turning it from its position of stable equilibrium to a position of unstable equilibrium in a uniform electric field \displaystyle \vec{E}.
Q.15
Define electric dipole moment. Write its S.I. unit.
Q.16
An electric dipole of dipole moment cm is enclosed by a closed surface. What is the net flux coming out of the surface ?
Q.17
An electric dipole with dipole moment 4 × 10–9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 NC–1. Calculate the magnitude of the torque acting on the dipole.
Q.18
A dipole, with its charges, –q, and +q, located at the points (0, –b, 0) and (0, +b, 0), is present in a uniform electric field \displaystyle \vec{E}. The equipotnetial surfaces of this field, are planes parallel to the y-z planes.
(i) What is the direction of the electric field \displaystyle \vec{E}?
(ii) How much torque would the dipole experience in this field ?
Q.19
A dipole, with a dipole moment of magnitude ‘p’, is in stable equilibrium in an electrostatic field of magnitude E. Find the work done in rotating this dipole to its position of unstable equilibrium.
Q.20
A dipole is present in an electrostatic field of magnitude \displaystyle {{10}^{6}}N/C. If the work done in rotating it, from its position of stable equilibrium to its position of unstable equilibrium, equals \displaystyle 2\,\times \,{{10}^{{-23}}}\,J, find the magnitude of the dipole moment of this dipole.
Q.21
An electric dipole is held in a uniform electric field.
(a) Show that the net force acting on it is zero.
(b) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180º.
Q.22
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 180º.
Q.23
An electric dipole of length 4 cm, when placed with its axis making an angle of 60º with a uniform electric field, experiences a torque of \displaystyle 4\sqrt{3}Nm. Calculate the potential energy of the dipole, if it has charge \displaystyle \pm 8\,nC.
Q.24
Two small identical electrical dipoles AB and CD, each of dipole moment ‘p’ are kept at an angle of 120º as shown in the figure. What is the resultant dipole moment of this combination ? If this system is subjected to electric field ( \displaystyle \vec{E}) directed along + x direction, what will be the magnitude and direction of the torque acting on this ?
Q.25
Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).
