Chapter 17

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion The electric field and hence electric field lines are everywhere at right angle to an equipotential surface. Reason Equipotential surfaces are closer together where the electric field is stronger and farther apart where the field is weaker.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion The plates of a parallel plate capacitor are connected to a battery. Charge on the plates increases on introducing a dielectric slab between the plates. Reason Capacity increases on introducing dielectric slab and hence more charge is drawn from the battery.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion When charges are shared between two bodies, there occurs no loss of charge. However, there is a loss in electrical energy. Reason Electrostatic potential energy does not come under the preview of the conservation law of energy.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion An electric dipole is placed in a uniform electric field. Its equilibrium will be stable when dipole is set along the direction of electric field. Reason In stable equilibrium energy of dipole should be least possible.

This question has Statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius \(R\) has a uniform positive charge density \(\rho .\) As a result of this uniform charge distribution, there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinity is zero. Statement I When a charge \(q\) is taken from the centre of the surface of the sphere its potential energy changes by \(\frac{q e}{3 \varepsilon_{0}}\). Statement II The electric field at a distance \(r(r

Combination of two identical capacitors, a resistor \(R\) and a DC voltage source of voltage \(6 \mathrm{~V}\) is used in an experiment on \(C-R\) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is \(10 \mathrm{~s}\). For series combination, the time needed for reducing the voltage of the fully charged series combination by half is (a) \(20 \mathrm{~s}\) (b) \(10 \mathrm{~s}\) (c) \(5 \mathrm{~s}\) (d) \(2.5 \mathrm{~s}\)

An electric charge \(+q\) moves with velocity \(\mathbf{v}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+\hat{\mathbf{k}}\), in an electromagnetic field given by \(\mathbf{E}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{B}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}} .\) The \(y\)-component of the force experienced by \(+q\) is (a) \(2 q\) (b) \(11 q\) (c) \(5 q\) (d) \(3 q\)

Two positive charges of magnitude \(q\) are placed at the end of a side 1 of a square of side \(2 a\). Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge \(Q\) moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is (a) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q Q}{a}\left(1-\frac{1}{\sqrt{5}}\right)\) (b) zero (c) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q Q}{a}\left(1+\frac{1}{\sqrt{5}}\right)\) (d) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q Q}{a}\left(1-\frac{2}{\sqrt{5}}\right)\)

Two identical charged spheres suspended from a common point by two massless strings of length \(l\) are initially a distance \(d(d \ll l)\) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity, \(v\). Then as a function of distance \(x\) between them, [AIEEE 2011] (a) \(v \propto x^{-1}\) (b) \(v \propto x^{1 / 2}\) (c) \(v \propto \underline{x}\) (d) \(v \propto \underline{x}^{-1 / 2}\)

A resistor \(R\) and \(2 \mu \mathrm{F}\) capacitor in series is connected through a switch to \(200 \mathrm{~V}\) direct supply. Across the capacitor is a neon bulb that lights up at \(120 \mathrm{~V}\). Calculate the value of \(R\) to make the bulb light up \(5 \mathrm{~s}\) after the switch has been closed \(\left(\log _{10} 2.5=0.4\right)\) [AIEEE 2011] (a) \(1.7 \times 10^{5} \Omega\) (b) \(2.7 \times 10^{6} \Omega\) (c) \(3.3 \times 10^{7} \Omega\) (d) \(1.3 \times 10^{4} \Omega\)

The electrostatic potential inside a charged spherical ball is given by \(\phi=a r^{2}+b\), where, \(r\) is the distance from the centre \(a, b\) are constants. Then the charge density inside the ball is [AIEEE 2011] (a) \(-6 a \varepsilon_{0} r\) (b) \(-24 \pi a \varepsilon_{0}\) (c) \(-6 a \varepsilon_{0}\) (d) \(-24 \pi a \varepsilon_{0} r\)

Let \(C\) be the capacitance of a capacitor discharging through a resistor \(R\). Suppose \(t_{1}\), is the time taken for the energy stored in the capacitor to reduce to half its initial value and \(t_{2}\) is the time taken for the charge to reduce to one-fourth its initial value. Then, the ratio \(\underline{t_{1}}\) will be [AIEEE 2010] \(t_{2}\) (a) 1 (b) \(\frac{1}{2}\) (c) \(\frac{1}{4}\) (d) 2

A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net field \(\mathbf{E}\) at the centre \(O\), is (a) \(\frac{q}{4 \pi^{2} \varepsilon_{0} r^{2}} \hat{\mathbf{j}}\) (b) \(-\frac{q}{4 \pi^{2} \varepsilon_{0} r^{2}} \hat{\mathbf{j}}\) (c) \(-\frac{q}{2 \pi^{2} \varepsilon_{0} r^{2}} \hat{\mathbf{j}}\) (d) \(\frac{q}{2 \pi^{2} \varepsilon_{0} r^{2}} \hat{\mathbf{j}}\)

Let there be a spherically symmetric charge distribution with charge density varying as \(\rho(r)=\rho_{0}\left(\frac{5}{4}-\frac{r}{R}\right)\) upto \(r=R\), and \(\rho(r)=0\) for \(r>R\) where, \(r\) is the distance from the origin. The electric field at a distance \(r(r

The question contains Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I For a charged particle moving from point \(P\) to point \(Q\), the net work done by an electrostatic field on the particle is independent of the path connecting point \(P\) to point \(Q\). Statement II The net work done by a conservative force on an object moving along a closed loop is zero. [AIEEE 2009] (a) Statement 1 is true, Statement 11 is false (b) Statement 1 is true, Statement II is true, Statement II is the correct explanation of Statement 1 (c) Statement 1 is true, Statement 11 is true, Statement 11 is not the correct explanation of Statement 1 (d) Statement 1 is false, Statement \(\|\) is true

Let, \(\rho(r)=\frac{Q r}{\pi R^{4}}\) be the charge density distribution for a solid sphere of radius \(R\) and total charge \(Q\). For a point \(P\) inside the sphere at a distance \(r_{1}\) from the centre of the sphere, the magnitude of electric field is [AIEEE 2009] (a) \(\frac{Q}{4 \pi \varepsilon_{0} r_{1}^{2}}\) (b) \(\frac{Q r_{1}^{2}}{4 \pi \varepsilon_{0} R^{4}}\) (c) \(\frac{Q r_{1}^{2}}{3 \pi \varepsilon_{0} R^{4}}\) (d) zero

A solid spherical conductor of radius \(R\) has a spherical cavity of radius \(a(a

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then [IIT JEE 2007] (a) negative and distributed uniformly over the surface of sphere (b) negative and appears only at the point on the sphere closed to the point charge (c) negative and distributed non-uniformly over the entire surface of the sphere (d) zero

A comb run through one's dry hair attracts small bits of paper. This is due to [Karnataka CET 2006] (a) comb is a good conductor (b) paper is a good conductor (c) the comb possess magnetic properties (d) the atoms in the paper set polarised by the charged comb

Two small spheres of masses, \(M_{1}\) and \(M_{2}\) are suspended by weightless insulating threads of lengths \(L_{1}\) and \(L_{2} .\) The sphere carry charges \(Q_{1}\) and \(Q_{2}\), respectively. The spheres are suspended such that they are in level with another and the threads are inclined to the vertical at angles of \(\theta_{1}\) and \(\theta_{2}\) as shown below, which one of the following conditions is essential, if \(Q_{1}=Q_{2}\) ? (a) \(M_{1} \neq M_{2}\) but \(Q_{1}=Q_{2}\) (b) \(M_{1}=M_{2}\) (c) \(Q_{1}=Q_{2}\) (d) \(L_{1}=L_{2}\)

A conductor has been given a charge \(-3 \times 10^{-7} \mathrm{C}\) by transferring electron. Mass increase (in \(\mathrm{kg}\) ) of the conductor and the number of electrons added to the conductor are respectively, \(\quad\) [AMU Engg. 2010] (a) \(2 \times 10^{-16}\) and \(2 \times 10^{31}\) (b) \(5 \times 10^{-31}\) and \(5 \times 10^{19}\) (c) \(3 \times 10^{-19}\) and \(9 \times 10^{16}\) (d) \(2 \times 10^{-18}\) and \(2 \times 10^{12}\)

The electric potential \(V\) at any point \(O(x, y, z\) all in metres) in space is given by \(V=4 x^{2}\) volt. The electric field at the point \((1 \mathrm{~m}, 0,2 \mathrm{~m})\) in \(\mathrm{V} / \mathrm{m}\) is (a) 8 along negative \(x\)-axis (b) 8 along positive \(x\)-axis (c) 16 along negative \(x\)-axis (d) 16 along positive \(x\)-axis

A parallel plate capacitor \(C\) with plates of unit area and separation \(d\) is filled with a liquid of dielectric constant \(K=2\), the level of liquid is \(\frac{d}{3}\), initially. Suppose, the liquid level decreases at a constant speed \(v\), the time constant as a function of time \(t\) is [IIT JEE 2008] (a) \(\frac{6 \varepsilon_{0} R}{5 d+3 v t}\) (b) \(\frac{(15 d+9 v t) \varepsilon_{0} R}{2 d^{2}-3 d v t-9 v^{2} t^{2}}\) (c) \(\frac{6 \varepsilon_{0} R}{5 d-3 v t}\) (d) \(\frac{(15 d-9 v t) \varepsilon_{0} R}{2 d^{2}+3 d v t-9 v^{2} t^{2}}\)

Two condensers of capacities \(2 C\) and \(C\) are joined in parallel and charged upto potential \(V\). The battery is removed and the condenser of capacity \(C\) is filled completely with a medium of dielectric constant \(K\). The potential difference across the capacitors will now be \(\quad\) [IIT 1988; Similar AMU (Engg 2009] (a) \(\frac{3 V}{K+2}\) (b) \(\frac{3 \mathrm{~V}}{\mathrm{~K}}\) (c) \(\frac{V}{K+2}\) (d) \(\frac{V}{K}\)

A uniformly charged thin spherical shell of radius \(R\) carries uniform surface charge density of \(\sigma\) per unit area. It is made of two hemispherical shells, held together by pressing them with force \(F\) (see figure) then \(F\) is proportional to [IIT JEE 2010] (a) \(\frac{1}{\varepsilon_{0}} \sigma^{2} R^{2}\) (b) \(\frac{1}{\varepsilon_{0}} \sigma^{2} R\) (c) \(\frac{1}{\varepsilon_{0}} \frac{\sigma^{2}}{R}\) (d) \(\frac{1}{\varepsilon_{0}} \frac{\sigma^{2}}{R^{2}}\)

Which of the following statement(s) is/are correct? [IIT JEE 2011] (a) If the electric field due to a point charge varies as \(r^{-2 s}\) instead of \(r^{-2}\), then the Gauss' law will still be valid (b) The Gauss' law can be used to calculate the field distribution around an electric dipole (c) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same (d) The work done by the extemal force in moving a unit positive charge from point \(A\) at potential \(V_{A}\) to point \(B\) at potential \(V_{B}\) is \(\left(V_{B}-V_{A}\right)\)

To form a composite \(16 \mu \mathrm{F}, 1000 \mathrm{~V}\) capacitor from a supply of identical capacitors marked \(8 \mu \mathrm{F}, 250 \mathrm{~V}\), we required a minimum number of capacitors. [Karnataka CET 2008] (a) 40 (b) 32 (c) 18 (d) 22