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Correct CHOICE is (a) q∫\(\frac {\lambda}{r^2}\hat{r}\)dl

The BEST EXPLANATION: Let the point charge is situated at a distance r from a small part dl on the LINE. The charge stored in stat small part=λ.dl. The force due to that small part will be DIRECTED towards the unit vector \(\hat{r}\). Therefore, force on that charge due to the entire linear charge distribution=q∫\(\frac {\lambda}{r^2}\hat{r}\)dl.

Right option is (a) [L T I]

For explanation I would SAY: The dipole moment is DEFINED as the product of a charge and distance. The dimension of charge (current*time) is [I T] and the dimension of distance is [L]. Therefore the dimension of dipole moment is [L T I]. Its unit in the CGS and the SI system are esu*cm and C*m RESPECTIVELY.

Right answer is (d) CH4

For explanation I would say: Though water and ammonia are covalent molecules, they have a net dipole moment due to their DISTORTED STRUCTURE than the ideal one. Hydrochloric acid has a linear molecular structure but its net dipole moment is towards the HYDROGEN ATOM. But methane has a symmetrical tetrahedral structure and its net dipole moment is zero hence it doesn’t behave as a permanent dipole. Methane SOLVENTS are therefore non-polar solvents.

Correct choice is (b) DIRECTED towards the CHARGE

Easy EXPLANATION: If a unit positive charge is KEPT NEAR a negative charge, the unit positive charge will be attracted towards the negative charge. That means the electric field is towards the negative charge. But in case of positive charge, the field is directed away from the charge.

Correct option is (d) INVERSELY proportional to r^2

Easy explanation: If the total charge of the SPHERE is q then the electric field at a distance of r is equal to \(\FRAC {q}{4\pi\varepsilon_o r^2}\).Therefore the electric field is proportional is \(\frac {1}{r^2}\) (if r > radius of the sphere). But if r < radius of the sphere the electric field will be zero i.e. electric field inside a hollow sphere is always zero.

Correct OPTION is (B) [M^0 L^-3 A T]

The best I can EXPLAIN: Volume charge density = \(\frac {charge}{volume}=\frac {CURRENT*time}{volume}=\frac {A*T}{L^3}\)=[M^0 A T L^-3]. But in case of surface charge density, the dimension will be [M^0 L^-2 A T] because surface charge density means an electric charge in a unit area of the surface.

The correct answer is (c) Zero

The EXPLANATION: The electric field is present in the y-z plane. So, if we place a square surface in the y-z plane, the area vector of the plane will be PERPENDICULAR to the electric field and hence cos⁡θ becomes 0 as θ is 90 degrees. So, E*surface area*cosθ becomes zero i.e. no flux through the surface.

Correct option is (b) -(∅1-∅2)εo

The best explanation: The net outward flux from the surface is (∅2-∅1) = -(∅1-∅2). We KNOW, according to GAUSS’s Law, net outward flux coming out of a CLOSED surface is \(\frac {1}{\varepsilon_o}\) times the CHARGE stored in it. Therefore charge stored in the surface = εo*flux coming out of the surface = (∅2-∅1)εo.

Correct ANSWER is (a) 180 degree

To explain: There is gravitational field on earth, so if we hang the two same charges there will be an interaction of vertical gravitational field and horizontal electric field. The SYSTEM will achieve equilibrium by creating a certain angle between the THREADS and hence the vertical and horizontal components of forces will balance. But in space, there is no gravity. So the charges will be at 180-degree separation.

Correct answer is (C) 5*10^-14 Coulomb

For explanation I would say: Charge of a BODY must be an integral multiple of charge of an ELECTRON.5*10^-14 is not an integral multiple of (1.602*10^-19 Coulomb) which is equal to the charge of an electron. But we can SEE that 4.8, 6.4, 3.2 are integral multiples of 1.6.

Right ANSWER is (a) 1.8*10^-8

For explanation I would say: A single Na^+ ION MEANS a single sodium atom without an electron. The charge of the ion is the same as the charge of an electron but positive i.e. +1.602*10^-19C. Therefore, applying Gauss’s LAW, electric flux coming out of the ion = \(\frac {charge \, of \, the \, ion}{\varepsilon}\). Substituting the VALUES, we get flux = 1.8*10^-8 Nm^2C^-1.

The correct answer is (b) False

Easiest explanation: We know that in the case of any conducting MATERIAL, the charge is always distributed on its OUTER surface instead of distribution THROUGHOUT the material. Therefore, the word volume charge density doesn’t MAKE any sense in the case of the conducting sphere. Instead, we can use the term surface charge density.

The CORRECT choice is (b) 15*10^-3 N. m

Easy explanation: Dipole moment of the dipole = 1*10^-6*5*10^-2 C. m=5*10^-8 C. m. Given the electric field-intensity is E=3*10^5 N/C. Therefore required TORQUE will be P*E*sinθ where θ is the angle between the electric field and the dipole moment = 90 degrees. Therefore torque required in this case will be 5 *10^-8*3*10^5*sin 90 N. m=15*10^-3 N. m.

Correct option is (c) Torque but no force

To elaborate: Dipole is the COMBINATION of two EQUAL but opposite charges, kept at a certain distance. If it is placed in a uniform electric field, both the charges will suffer the same but opposite forces on them. As a result, the net force on the dipole BECOMES zero, but due to equal and opposite forces ACTING on two DIFFERENT points, there is a net torque acting on the dipole.

The correct ANSWER is (b) 4πR^2 N∈

Easy explanation: Field lines come out from the surface. That means the charge must be POSITIVE. According to Maxwell’s principle, field lines COMING out from a charge q is equal to \(\frac {q}{\EPSILON}\) where ∈ is the relative permittivity. The total number of field lines coming out of the SPHERE is 4πR^2N. This must be equal to \(\frac {q}{\epsilon}\). Therefore q=\(\frac {4\pi R^2}{N\epsilon}\).

The correct option is (d) Force is inversely proportional to the distance between the bodies

Best EXPLANATION: Gravitational force cannot be REPULSIVE and it is a very WEAK force. Gravitational force does not depend on the medium. But both the FORCES are inversely proportional to the distance between them.

Right OPTION is (c) Same

For explanation I would say: If the radius of the BALLOON is 2 times the initial value, the surface area of the balloon will be 4 times the initial value because of surface area=4π(radius)^2. But in this case, flux COMING out from the balloon is dependent only upon the charge inside the balloon, not on the area of the surface. As charge enclosed in the balloon is the same in both the cases, the flux will also be the same.

The correct OPTION is (d) Zero

Easy explanation: According to Gauss’s principle, if there is no charge bound INSIDE a surface, net electric FLUX coming out of the surface will always be 0. In this case, the charge is kept outside the surface, so it will GENERATE no field LINES and hence no flux inside the surface. The situation will be the same if an electric dipole is placed inside a surface as dipole has equal positive and negative charges; the total charge inside the surface becomes 0.

The correct CHOICE is (d) \(\frac {q}{8\varepsilon_o}\)

To explain: We can assume 8 imaginary cubes, all of side a placed together, sharing a common CORNER point and forming a bigger cube of side 2A. The point charge is placed at the common point of the cubes. ACCORDING to Gauss’s Law, net electric flux coming out of the bigger cube=\(\frac {q}{\varepsilon_o}\). THEREFORE, flux coming out from each of the smaller cubes i.e. cubes of side a is \(\frac {q}{8\varepsilon_o}\).

Correct answer is (b) Only due to the charge INSIDE that point

The best explanation: In the case of a non-conducting sphere, an ELECTRIC charge is uniformly distributed THROUGHOUT the sphere. Inside the sphere, the electric field at a point will be only due to the electric charge inside that point. There will be no effect of the REMAINING charge outside that point. In the case of the conducting sphere, the electric field at every point inside the sphere is zero.

Correct choice is (b) 2.77*10^10

The explanation is: The electric field E = k \(\frac {Q}{R^2}\) where k=9*10^9 N m^2 C^-2 and Q is the charge of the sphere, r is the radius of the sphere. Therefore Q = \(\frac {E*r^2}{k}=\frac {1000*0.2^2}{9*10^9}\) = 4.44*10^-9. NUMBER of electrons REQUIRED for this amount of charge is = \(\frac {4.44*10^{-9}}{1.602*10^{-19}}\) = 2.77*10^10.

Right CHOICE is (a) A net DIPOLE moment will be observed

The best I can explain: A non-polar substance consists of a HUGE number of dipoles in it, but they are oriented randomly and hence the net dipole moment of the substance becomes 0 and it ACTS as a non-polar substance. But if it is placed in an electric field, the dipoles present in it will ORIENT themselves in the direction of the field and hence a net dipole moment will be observed, known as induced dipole moment. No current flow or oscillation of the substance will be observed.

Correct CHOICE is (b) E1=2 E2

Explanation: If the dipole moment of a dipole is p, then electric field INTENSITY at a distance r from the dipole on its axis will be \(\frac {2p}{r^3}\). But electric field intensity at a distance r from the dipole on its perpendicular bisector is \(\frac {p}{r^3}\). Both the formulas are DERIVED by assuming r >> length of the dipole. THUS E1=\(\frac {2p}{r^3}\) and E2=\(\frac {p}{r^3}\) and hence E1=2 E2.

The correct choice is (C) Is zero

To ELABORATE: According to Gauss’s law, if there is no charge inside a closed surface, the field inside the closed surface will always be zero. We know the charge is distributed on the OUTER surface of a conducting hollow sphere because the charges want to maintain maximum distance AMONG them due to repulsion. So there is no charge inside the sphere and hence no ELECTRIC field.

Right choice is (c) Coulomb force is a weak force

The best EXPLANATION: Coulomb force is a strong force. It can be shown that the Coulomb force between TWO electrons is 10^43 TIMES than GRAVITATIONAL force. All the other options are basic properties of Coulomb’s Law.

Correct choice is (a) Stat COULOMB

For explanation: The C.G.S. UNIT of charge is Stat Coulomb or ESU but in the SI SYSTEM the unit is Coulomb. EMU is ANOTHER unit of charge in the SI system. Pascal is the unit of pressure.

The CORRECT OPTION is (c) \(\frac {(m*g)}{e}\)

Easiest explanation: Gravitational force on the electron is m*g (weight of the electron). Electrical force on the body is e*E. If the electron doesn’t FALL then these two forces BALANCE each other, so m*g=E*e. Therefore E= \(\frac {(m*g)}{e}\).

The correct choice is (a) Electric field intensity

For explanation: The zone near a CHARGE where its attraction or repulsion force works, is known as the electric field of that charge. THEORETICALLY, it is up to INFINITE but practically it has limitations. If a unit POSITIVE charge is kept in that field, it will undergo some force which is known as electric field intensity at that POINT.

The CORRECT option is (a) 1 dyne/esu

To elaborate: We know that electric field intensity at r distance from a point charge q is DEFINED as \(\frac {q}{r^2}\) in the CGS SYSTEM. Here q=100 esu, r=10cm. Substituting the value we get E=1dyne/esu. We must remember that factor \(\frac {1}{4\pi\varepsilon}\) is CONSIDERED only in the SI system and its value is 9*10^9, but in the CGS system, we simply take the value of this constant as unity.

Correct option is (a) Electron

Easy EXPLANATION: Conductors have LOTS of free electrons that can CARRY electricity if the potential difference is applied across them. Protons are positively CHARGED PARTICLE and Neutron are electrically neutral. They don’t carry electricity in conductors.

Correct choice is (c) NEEDLE END

Explanation: Needle end can arrest the LIGHTNING easily. Besides, the device must provide a CONTINUOUS path to electricity so that current passes to ground. It must have a high melting point else it will meltdown due to the HEAT generated during carrying lightning current.

Right answer is (B) π*a*(R^2-r^2)

For EXPLANATION I would say: Total surface area of the ANNULUS = π*(R^2-r^2) because it has outer radius R and inner radius r. We know surface CHARGE density is the amount of charge stored on the unit surface area. In this case, surface charge density is a. THEREFORE total charge on the annulus = π*a*(R^2-r^2).

The correct answer is (a) True

To elaborate: If we observe the structure of the CO2 molecule, we will find that the two C=O bonds are not in a STRAIGHT line DUE to the PRESENCE of lone pair of electron of C atom. Therefore the dipole moments of the two C=O bonds don’t cancel out each other and hence there is a net dipole moment present in case of CO2 molecule. It means the center of POSITIVE and negative charge does not coincide in the case of polar molecules.

Correct choice is (d) ZERO

Explanation: The magnitude of the force acting on each of the charges will be the same and they will differ from each other by 120 degrees. THEREFORE their resultant force will ALWAYS be zero.

Right choice is (a) 9*10^9 N

To explain: The FORCE on 1^st charge will be = 9*10^-9*(\(\frac {1}{\sqrt{2}^2} + \frac {1}{\sqrt{4}^2} + \frac {1}{\sqrt{8}^2}\) +⋯) = 9*10^-9*\(\frac {\frac {1}{2}}{1-\frac {1}{2}}\) = 9*10^-9N [INFINITE GP formula].

The correct choice is (a) 0 degree

Easy explanation: Torque ACTING on a DIPOLE is p*E*sinθ where E is the electric field. Now θ is 0 degree, so sinθ becomes 0 and hence no torque acts on the dipole. So in this case, no force or torque acts on the dipole. Therefore it will be the CONDITION of stable equilibrium. In the case of θ=180 degree, sinθ is ALSO 0 but the condition is known as unstable equilibrium i.e. if we rotate the dipole a bit, it will not come back to its initial position.

Right choice is (a) The conductivity of the material

Easiest explanation: The more the BAND gap between the VALENCE band and conduction band, the worse is the conductivity of the material. For conductors, there are overlapping bands. So, conductors can carry ELECTRICITY. But there is a HUGE energy gap in the CASE of insulators. So, they don’t carry electricity at all.

The correct choice is (a) \(\frac {4\pi}{k}\)

Best explanation: In the SI system, Gauss LAW states that flux= (\(\frac {1}{\varepsilon_o}\))*electric CHARGE. But is the CGS system, the law states that, flux= \((\frac {4\pi}{k})\)*electric charge [where k is the DIELECTRIC constant of the medium]. Therefore we have to replace (\(\frac {1}{\varepsilon_o}\)) with (\(\frac {4\pi}{k}\)).

Right answer is (b) False

To elaborate: We know, the torque acting on a dipole of moment p and placed in a field E is equal to \(\VEC{p} \times \vec{E}\) which can also be written as p*E*sinθ following the CROSS product RULE. In this CASE, the field is parallel to the axis of the dipole. Therefore θ=0 and sinθ is also equal to 0. Hence, the torque acting on the dipole will be the minimum i.e. 0. The torque will be maximum if θ=90 DEGREE and so sinθ becomes 1 in that case.